Well, first of all, banks cannot simply claim that they don't have all your money available and give you back only half instead. Once they reach a stage where that is their problem, they are bankrupt, and you get to sell their assets to recover your money.
I think it's much simpler in the case of ISPs, because there is no risk involved for the customer: You don't need to regulate how much they can oversell, but rather simply that the customer must not ever notice that the network is oversold.
First of all, only paying out part of the balance at once is very different from paying out part of the balance instead of the full balance. A bank can not unilaterally declare that their 100 dollar debt to you is paid by giving you 50 dollars. If they pay out 50 dollars, they still owe you 50 dollars.
But more importantly: No, they can not even unilaterally delay the payout. If you have demand deposits of a million bucks with a bank, that means that you can at any point demand they pay out a million bucks, and when you demand that, they are legally required to do so, and if they can't fulfill a legal obligation to pay, that is exactly the definition of bankruptcy. If they fail to immediately declare bankcruptcy, the management is on the hook for any losses due to that failure of theirs.
Banks might limit what their ATMs pay out per person per day or something, say, but that does not change anything about their obligation to fulfill any requests to pay out your balance immediately. Just because the ATM doesn't allow you to demand a payout of a million dollars, doesn't mean they have any legal option to refuse if you go to the cashier and express your demand that they pay out a million dollars right now. At best they might not have a million dollars on site, in which case they possibly might be allowed to have you wait for however long it takes to move the cash from the central bank to the branch that you are at, but that is certainly not more than a day.
You're right that the bank cannot unilaterally prevent a payout.
Practically speaking though, what usually happens during a potential bank run is that governments declare a bank holiday, preventing customers from withdrawing funds.
That buys the government (and the bank) time to get their ducks in a row, line up bailouts, etc.
Things get a LOT worse if the bank is actually allowed to go under. Letting Bear Stearns and Lehman collapse was, in retrospect, probably a mistake that made the eventual bailout need to be larger.
Well, that really depends on the bank, though. In the case of smaller/local banks, chances are that it will simply go bankrupt to be wound down and deposit insurance will pay out the balance (or as much of it as is insured) within a couple days.
But also, bankruptcy does not necessarily imply that the bank collapses: One way to resolve a bankruptcy is to obtain funds, possibly in the form of a bailout, that allow any demands to be fulfilled. Rather, bankruptcy is exactly the thing that allows the bank to refuse payouts even when it's not a bank holiday. The point is that once a bank has declared bankruptcy, it is not allowed to pay out to anyone anymore without oversight, because the bankruptcy proceedings are supposed to make sure that everyone that the bank is indebted to gets a fair share of the remaining assets--or possibly to find a solution that allows the bank to resume operations by accepting a later payout for some of its debts. The important point in all of this is that in any case, none of this can be used directly to increase the equity of the existing owners. If the bank has to obtain loans in order to fulfill its obligations, the interest on that is paid from equity. If there is no equity, the bank changes ownership (like, if the state bails out the bank, the state gets to own the bank). So, even if the bank might refuse to pay out under certain circumstances, the processes that get triggered by that have as their primary goal to make those payouts happen as soon as possible, not to allow the bank's owners to keep anything.
I think it's much simpler in the case of ISPs, because there is no risk involved for the customer: You don't need to regulate how much they can oversell, but rather simply that the customer must not ever notice that the network is oversold.