Yes, if the house is older, has large trees, or has a history of
backups. A general home inspection does not usually include the buried
sewer line.
The sewer lateral is the pipe from the house to the public main, and
its owner pays for repairs.
Snyderville Basin Water Reclamation District,
which serves the Park City area, states that the private property owner
is fully responsible for the entire length of the lateral, from the
building to the connection at the main.
Jordan Basin Improvement District,
in the south Salt Lake Valley, says the district is responsible only
for its own property, not your line or your connection to the main.
A broken lateral becomes the buyer's bill the day the sale closes. An
inspection before closing shows the pipe's condition while there is
still time to negotiate.