Stagflation is hard to fight. Raising rates to cool prices can hurt jobs further, and cutting rates to help jobs can push inflation higher, so the Federal Reserve has no easy option.
A sudden rise in energy prices is the classic cause. It tends to be bad for both stocks and bonds, because profits and the value of fixed payments suffer together.
Example
The US in the 1970s: oil shocks pushed inflation into double digits while unemployment climbed.