Thank you for allowing us to assist you with this problem.
I'm sorry to hear that you are in this difficult situation.
Probate itself does not stop foreclosure. The probate process may slow down the process if the executor/executrix gets involved and negotiates with the lender, but it is not the same as a bankruptcy action which may stay a forclosure for awhile.
when a shareholder dies, the co-op apartment is passed on to a spouse or children as a matter of course. Often, an heir, whether a member of the immediate family or not, will sell the apartment.
The proprietary leases of most co-ops give spouses the automatic right to take over an apartment after the death of the named shareholder.
When it comes to children, the lease usually makes a distinction between spouses and children, the board cannot unreasonably withhold the right of offspring to occupy apartments they have inherited.
So the simple answer to your second question is that should the fees not be paid it is possible that the board could take the coop shares.
I hope you find that this information answers your questions,