Rights to the deceased's estate?

If the will does not dispose of it, then it depends on the intestacy law of the state. Also assuming that the unit owner doesn't jointly own it with right of survivorship. BTW, it may not be New York even if the co-op is situated here.

A few examples (NY State):
1) No living descendants, but you have a spouse -> all to living spouse
2) Children & spouse (no predeceased children) -> 50k + half to spouse (though I'm not sure how it's calculated if only the co-op is not in the will), remainder divided between children.

More examples http://www.mystatewill.com/statutes/ny_law.htm

If this unit is a co-op, you should first look into the deceased owner's stock certificate and / or proprietary lease to determine if anyone else has an ownership in the stock. If there are additional owners listed on the stock certificate, how the stock will be spread out will depend on whether the stock is owned as tenants by the entirety, tenants in common, or joint tenants. Tenants by the Entirety applies only to Husband and Wives. Joint tenants are reflective of the survivorship of those on the lease and the surviving owner would take title to the stock. If the stock was owned as tenants in common, the decedent's interest in the stock would become part of the decedent's estate. TIC (tenants in common) would essentially mean that the stock will go to whomever was stated in the decedent's will. If the decedent has no will, then more than likely a relative will inherit the estate. (generally taken to court to be decided) I believe laws provide that the spouse comes first, and the remaining property can be split between the children. If no spouse or children are involved, then the parents are next in line.

WIth all that being said, if this property you are speaking of is a co-op, then you will still have to apply with a board package, and get permission from the board to become a shareholder and occupy the apartment. (obviously subject to terms, conditions, and the type of building / co-op board)

BTW, it would be exceedingly difficult for the deceased's ownership interest to be left out of most "boilerplate" wills. Because the language of the will usually includes a catch-all phrase, like "my property" which would include the co-op shares.

I'm not an attorney, so don't put too much faith in my answer ...

If the will was drafted with the help of an attorney, or using a standard boilerplate, it will almost certainly refer to "real property", whether or not the person owned an apartment ... a properly drafted will covers all bases, real or potential.

I'm assuming that where the law is concerned regarding wills, a coop is real property. Typically, from what I've seen, wills call for property to be sold and the proceeds allocated as specified in the will, which usually has cascading scenarios in case the named parties predecease the, um, deceased.

In any event, I wouldn't expend too much energy on this until the will is read.

My own will, for example, has a section that reads as follows:

TWO: RESIDENCES

I direct that (i) all real property used by me for residential purposes (including any buildings and improvements thereon), and (ii) all cooperative apartments used by me for residential purposes (including the shares of stock and proprietary leases relating thereto) be sold and that the net proceeds of sale be disposed of as a general asset of my estate.