If the tenant won't leave by closing day, can I still be forced to complete my purchase?

Generally, yes, unless your Agreement of Purchase and Sale specifically made vacant possession a true condition of your obligation to close. Your obligation to complete the purchase and the seller's obligation to deliver vacant possession are often treated as separate issues, so a tenant remaining in place does not automatically excuse you from completing, particularly if the agreement is silent or only loosely addresses tenancy status.

This is exactly why the wording of your agreement matters so much. If vacant possession was clearly made a condition you can rely on, a tenant still in place may allow you to delay or refuse closing and pursue the seller for breach instead. If it was not, you may need to complete the purchase and then deal with the tenancy yourself as the new landlord, potentially pursuing your own remedy against the seller separately for failing to deliver what was promised. Because this depends entirely on specific contract language and timing, review your agreement with your lawyer as soon as it becomes clear the tenant will not be out, rather than waiting until closing day itself to find out where you stand.