In the RAW rules, a crafty Axis player can not only delay any Italian surrender check for an extended length of time, the Axis player can also control when that check is made to a much greater degree than would seem appropriate given the historical situation and record. This Fascist Collapse rule attempts to address both of these concerns.
Basically, the rule assumes that Allied ownership of Sicily is enough to trigger the sequence of events which lead to the overthrow of the Fascist regime in Italy. Once the Allies control Sicily [in game terms, once they own all ports and cities on Sicily and there are no Axis units there in regular supply] the Allied player may check for the collapse of Fascism in Italy at the END of any Allied player turn in which Sicily is controlled by the Allies.
At the end of each Allied player turn in which Sicily is Allied controlled the Allied player rolls a die, modifies it as appropriate and if the die roll is six  or greater, then Fascism has collapsed in Italy. The effect of this Fascist collapse is that the Capital of Italy is treated as having been captured by the Allied player – note that this is a Surrender condition and is treated, for the purposes of this rule [only] exactly as if the Allies had captured the Italian capital. Note that since Allied Control of Sicily is also a surrender condition [and must have occurred for this special house rule to have been implemented], if the Allies control Sicily AND have caused the collapse of Fascism in Italy then a surrender check will be made during the next Axis initial phase.
Note that this house rule ONLY affects Rule 38.B.2 and is not considered for purposes of Rules 37.G or 38.B.1. The effects of a capital being captured by the enemy player, such as morale, do not apply due to the collapse of Fascism.
There are two possible modifiers to the die roll for the collapse of Fascism in Italy:
each turn following the first turn that Fascism could collapse in Italy, a cumulative +1 DRM is applied to the die roll. So during Fascist Collapse 1 [i.e. the player first turn in which the Allies control Sicily] will have no DRM. During Fascist Collapse Turn 2, a +1 DRM would be applied, during Fascist Collapse Turn 3; a +2 DRM would be applied, and so on.
during any Allied player turn in which the Allies have more than 3 REs of units in regular supply in Mainland Italy, a +1 DRM is applied to the Collapse of Fascism die roll.
Example of play: The Allies control Sicily by the end of their Aug II player turn but have no units in regular supply in mainland Italy. This allows the Allies to check for the Collapse of Fascism at the end of their Aug II player turn. This is Fascist Collapse Turn 1. Since there are no Allied units in regular supply in mainland Italy, no DRM’s apply to this die roll and Fascism in Italy would collapse on a die roll of six . The Allied player rolls a 3 and Fascism in Italy does not collapse. Assuming that the Allies still control Sicily and still have 3 or fewer REs of units in regular supply in mainland Italy, Sep I will be Fascist Collapse Turn 2, and a +1 DRM will be applied to the Allied player’s die roll at the end of their Sep I player turn. Thus Fascism in Italy will collapse on a die roll of five  or six  due to this turn’s automatic DRM of +1. The Allies roll a one  and Fascist Collapse in Italy does not occur. Still assuming Allied control of Sicily and insufficient Allied units in supply in mainland Italy, Oct I will be Fascist Collapse 3 [and there will be a +2 DRM to the Fascist Collapse die roll, Oct II would be Fascist Collapse 4 [with a +3 DRM] and so on.
In this example note that Fascism in Italy would collapse automatically during the Axis Nov II initial phase, since there would be a +5 DRM – even a die roll of one , in this case, would be modified to a six  due to the automatic +5 DRM. The historical situation would be that the Allies control Sicily by the end of their Aug II player turn. Thus Aug II is Fascist Collapse Turn 1 and the Allies are lucky enough to roll a six  and Fascism Collapses in Italy. The Axis would be forced to check for Italian surrender during their Sep I initial phase, since the Allies have fulfilled two surrender conditions, namely control of Sicily and having forced the collapse of Fascism in Italy. The Allied player rolls the die to check for Italian Surrender [as per Rule 38.B.2], rolls a three  and Italy surrenders.
The intent of the rule is to add another random factor into the procedure for modeling Italian Surrender. The Axis player should not be allowed to control when Italian surrender occurs [as he can now, to a large degree] and further, he should not know precisely when a surrender check will have to be made. The Allied player is rewarded for attempting to capture Sicily [as was historical] but he is also not overly penalized for not taking Sardinia and Corsica. As the RAW stands now, the Axis player can easily protect the Italian Army enough such that they will not suffer 50 REs of losses [a surrender condition] until after the Allies take Sardinia and Corsica – this pretty much insures that the first surrender check will be triggered not by Allied control of Sicily and 50 REs of Italian losses [as was historic] but rather will be delayed until the Allies control Sicily AND Sardinia & Corsica.
This sequence of events serves to severely distort the game as it stands now – the Allied player, knowing that he will not be able to inflict 50 REs of losses on the Italians in any sort of reasonable amount of time, is forced to invade and control both Sardinia and Corsica before any surrender check can be made. Corsica, in particular, can be a very hard nut to crack due to the broken terrain there, but the Allies have no real alternative other than conducting a campaign there. Historically, neither Corsica or Sardinia were taken before Italian surrender so it seems to me that we have to provide some mechanism for a possible Italian surrender that does not depend so completely upon the capture by the Allies of Corsica/Sardinia.
The house rule also makes a wholesale Sicilian Runaway defense less attractive to the Axis, since the loss of Sicily will not only be a surrender condition [as it is under RAW] but will also lead, ultimately, to the collapse of Fascism in Italy and thus another surrender condition. Thus abandoning Sicily without a fight is not quite the “no brainier” tactic that it is now.
The overall effect of the rule will be, I hope; that Corsica and Sardinia will no longer be the main focus once Sicily is Allied Control, abandoning Sicily will be less attractive as an Axis option, Italian Surrender will be somewhat more randomized and that the current situation where the Axis player can, in effect, control when Italian surrender occurs will be altered in the Allied player’s favor. Italy had historically suffered huge manpower and territorial losses by the time frame of the game and were certainly well on the road to collapse, if not teetering on the edge of surrender by Summer ’43. Mussolini was, after all, overthrown before the end of July and Fascism was on its last legs at this time. The rule assumes that Mussolini is deposed pretty much as happened historically[which happened due to the Allies successfully LANDING on Sicily, not controlling it…] and that Fascism does not long survive his fall.