When installing a new sewer line at my house, the goal is a complete 4"
sch40 PVC mainline connection from the house to the curb, except that, in
one small section, in which a concrete staircase is over the pipe, they're
considering slipping the 4" PVC through through the existing 6" clay pipe
(assuming the current outside line is 6" clay.)

The line within my house is already only 4" line, and 4" PVC is what they
normally install around here for new residential lines as permitted by the
code. If so, then slipping the 4" Sch40 PVC through existing 6" clay pipe
is being considered for the problematic section where the concrete steps are
located. The end result would be a completely-PVC connection from my house
to the curb, except that one section of the PVC pipe would happen to have
the old 6" clay pipe around it.

Would this be considered improper or is this acceptable?

Jeff