Ron wrote:

I would contact the local building inspection department to see if there
is any way to have it inspected after the fact. If there is, insist
that the seller do this, and correct any violations, before you close.
If not, insist that the seller pay to have the basement checked out by a
qualified building inspector and pay for any safety problems uncovered.

Chuck

Having just sold and bought a house, the buyer pays for any inspection that
he wants. The seller's obligation is to disclose truthfully what he knows
about the property.

At least around here that is the how it is done.

If finishing the basement requires a permit and the seller did so
without one then what they have done is ILLEGAL. This could create a
mess for the buyer. In a situation like this it should be up to the
seller to prove that the improvements were done safely.