I don't think such a measure is used, nor it would be particularly useful. The fact that you have $X left over in your bank account at the time of closing says nothing at all about what level of savings you will have the very next day - you could go out and buy $X worth of furniture the day after closing. Prior to closing, a bank wants to see that you have sufficient funds for the down payment, and sufficient income to make installments on the loan. A modest lump sum leftover after the down payment obviously doesn't help make the down payment, and while it may cover the bills for a few months, it is not good evidence that you can make regular payments for years on end.
For it to be useful, the bank would need to see a continuous minimum balance in your account, not just a lump sum at the time of closing. But no bank that I know of enforces an obligation that borrowers maintain some minimum level of cash savings on an ongoing basis.
In one sense, mortgage lenders may require additional ongoing savings in the form of escrow. Typically, funds in escrow are earmarked for taxes and insurance and are effectively pre-payments of these bills, assuring the lender that it is essentially impossible for you to fall behind on these payments for several months into the future. Failure to pay taxes and insurance can have serious consequences outside the mortgage company's control, so it is a means of protecting their interest in your property.