Will restaurants actually allow you to wash dishes as compensation if you cannot pay? No, they won’t.
If you don’t have the money to pay for a meal that you have eaten, one of three things will happen:
The restaurant will ask you to leave something that you’ll return for when you have retrieved the funds to pay them.
Depending upon the mood of the owner, the amount of the bill and the reasons that you have forgotten your method of payment, they may simply say forget it and comp you your meal. This will rarely happen and no one should expect this to occur when they dine out.
They’ll call the police and have you cited or arrested for fraud. Defrauding an innkeeper is a serious offense in a number of states, so you may find that your meal costs you far more than had you simply paid for it in the first place.
Some advice: If you find yourself in a situation where you don’t have the money or another means (accidentally) to pay your tab, call a friend or a family member and have them come and bring you some money to do so. The restaurant can wait for this to happen (as long as it is a reasonable amount of time) and it will avoid the police being called.