Hanging onto a precious rent-stabilized apartment can feel tenuous enough as is, and if the landlord kicks the bucket while you're living there? Well, we'd understand why a tenant would get nervous.
"[Our landlords] are elderly and will someday pass and their grown sons have no interest in taking over the building when that happens," a pair of rent-stabilized Greenpoint renters wrote into Gothamist's Ask A NYC Housing Lawyer column. "Whenever this building changes hands, how feasible is it that all of the current tenants would be safe from getting thrown out?"
The answer, in a nutshell: they can likely stay put, but not without a fight.
The landlords' sons may try a number of well-worn tactics to get the rent-stabilized tenants out, though they're complicated by the fact that most of the other renters in the building are rent-controlled, rendering them nigh impossible to kick out. It's possible for the landlords' sons to claim "owner use"—i.e. that they need your unit for their family—which is, indeed, a perfectly legal way to give stabilized tenants the boot (provided family members are actually moving in, that is). They could also try to evict on the grounds that they plan to demolish the building, and re-build to include more units.
However, both of these tactics are massively complicated by the presence of rent-controlled residents in the building, and if the new owners are hoping to clear the place out entirely and sell to investors, they're more likely to resort to standard issue harassment: disruption of services, noisy construction, veiled threats, etc. In that case, there's strength in numbers, and residents would be wise to form a tenants' association, and if necessary, take their complaints to the city (and likely, a lawyer).