Once a person has terminated a lease in a apartment and they remain there, can they be locked out and are they criminally trespassing?

I guess, in a sense, you could be considered a 'squatter'. Yes, you would be trespassing.

If they were previously a tenant then they are now considered a "holdover" tenant. The penalties depend on the terms contained in the previous lease and also state law. But they cannot be locked out. When a landlord locks out a tenant that is considered an illegal eviction. The landlord must follow state law for evicting a holdover tenant.

I would want to hear more details on this. Did they actually state they were terminating the lease did it just expire. Did they change their minds and decide to stay? Did the landlord rent to someone else?

As Lisa said, a lockout is illegal. Only after a court order of eviction can a tenant be locked out and then, it has to be done by a sheriff, not the landlord.

If they were a renter and just did not leave after giving notice, they are still have a tenantcy estatblished and you can not just lock them out.
They would have to be given notice and evicted though the courts

Now if they had completely moved out, but latter returned and is merely a tresspasser, then you call the police.