As if things weren’t bad enough for the auto industry, now used-car prices are cratering. That creates more pressure in several areas of the automotive value chain.

The Manheim Used Vehicle Value Index—a key benchmark for industry pricing—has declined about 11% compared with March and is down roughly 10% year over year. The last time the Index dropped a similar magnitude was, unsurprisingly, during the 2008-09 financial crisis.

The...