I dont know about NY, but I can't see how the two are related. Owning RE is an investment, not a job. Getting laid off from your job is what makes you available for unemployment insurance.
Be safe, ask a subject matter expert in your state.
Look up what is required to collect unemployment. It's been a long time since I collected it, but as I recall, it has nothing to do with your assets. It's based on whether or not you are available for full-time work, and if you have enough work credits in your account.