I agree that you will need to look at your proprietary lease. Generally, however, the managing agent will send out a notice that if the individual tenants do not remove their property from the communal hallway within a certain stated time frame, someone will remove the property and perhaps store it in the basement (if space is available) for a short period of time to allow the owner to claim it. Thereafter, it could be thrown out, or if it has value, donated to charity. If your building does...
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The by-laws of the condominium should address your question.
Landlord could not do this in New York; hopefully, a Texas attorney will respond.