If the tile (asbestos of nay) is in good shape (which I assume if you are
thinking of painting) and not deteriorating,  why does the owner feel it needs
encapsulating?  Several coats of wax is sufficient for residential basement
use.  I see no need to remove it or otherwise unless the owner is simply tired
of looking at it and wants to remodel.  Painting is an inexpensive choice, and
one the owner can do themselves if willling. I would recommend the usual
removal of any old finishes, waxes, etc and use several coats of a good sealer
(Bin has seen some good results), paint and clear seal again (some of the
waterbased sealers aren't too bad if over acrylics.  Painted floors will last
years if the prep is carefully done and top finishes can be dressed often.
If the owner can't be bothered - go over it with a new floor.
Panic about asbestos bothers me.
Candy B