It's not clear what you mean by an "execution of stay."
You cannot be evicted without a judgment of possession in favor of the landlord.
If you were still resident in the apartment, that judgment could be acted upon other than by a sheriff who would evict you according to the law (which, not incidentally, includes a provision mandating storage of some or all of your effects.)
If the landlord took it upon himself to move all of your things and take possession WITHOUT the assistance of a sheriff, he's probably made a serious and potentially costly mistake. You may be able to recover damages. You should contact a landlord/tenant attorney for a free consultation, and explain the details of your case.
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I think you may be referring to the fact that your landlord obtained an execution. A tenant in your circumstances would seek a stay or postponement of that execution under certain compelling circumstances such as disability in order to postpone removal by the sheriff. Even with an execution, a landlord cannot engage in self-help and must have you properly and legally removed, including the removal of your belongings, by a sheriff with the assistance of a licensed moving company. If your landlord has engaged in self-help and/or there are compelling reasons you should be granted additional time to vacate, you should seek immediate assistance of counsel and, at the very least, injunctive relief and/or file a motion for stay of execution. Often, especially if you are behind on your rent, you will have to pay your landlord immediately a sum determined by the court in order to postpone removal. Stay of the execution isn't automatic and a court may not consider your circumstances particularly compelling. If you have any questions, you should consult an attorney or legal services.
This "answer" is for information purposes only and is not intended as legal advice or to create an attorney-client relationship.