If you simply drive for a garage, or under someones elses cab, don't worry about it unless you were drinking, then you are screwed. You will usually only owe the deductable, and most garages will let you work off repairs.

If you leased the medallion and owned the cab, and moreso if you owned the medallion and owned the cab, you should have created an LLC or a S/C corporation that would own the medallion (if its yours) and/or the cab. That places some distance between you and a bad accident.

But in reality, there is no way to 'reduce' liability after an accident- unless the God that you pray to answers your prayers, and the afflicted do not sue. Either way, sue or not, an accident will show up on your record, a really high payout might not make the insurer too likely to renew you if you have your own cab.

The only way to 'reduce' liability is to do so before an accident- by forming an LLC or and S/C Corp and having your LLC or S/C corp own everything- the medallion, the cab, etc, that way if you are found liable for more than the insurance, they get squat unless there is equity in the medallion. What's more, they usually won't try to sue for more, unless you were drinking, since personal assets can only be touched if you were drinking.

And if you were drinking and caused this accident, then I hope you get wiped out financially. If not, you know in the future to form an LLC or C/S corp, then you won't need to worry at all. The most they can get is the assets in the corporation, and usually they only get the insurance payout.