A once politically far-fetched question — can President Biden be replaced at the top of the Democratic Party presidential ticket — has taken on new urgency after Mr. Biden’s halting debate performance against former President Donald J. Trump.

The short answer is yes — assuming Mr. Biden decides on his own to step aside. But if Mr. Biden decides not to step aside, the short answer is probably no.

Either way, the process would be complicated and would open the door to political upheaval between now and when Democratic delegates gather to vote for a nominee at their convention in August.

Mr. Biden has the power to leave the race and release all the pledged delegates he has accumulated — 3,894 of 3,937 committed so far, according to a tally by The Associated Press — during his march to the nomination. If he were to do so, those delegates would be free to vote for whomever they chose. That would lead to an open convention, a rarity in modern American politics.

The prospect raises many questions.

Could President Biden, should he decide to drop out of the race, compel his delegates to support a candidate of his choosing?

No. He could certainly endorse a successor, and that would count for something. But once the delegates are free, they are free. Loyalty to Mr. Biden, which runs deep, does not automatically extend beyond him. And there could be a floor fight over who would emerge as the nominee, highlighting already festering ideological divides in the party, and potentially weakening a future Democratic candidate heading into the fall campaign.