Peony tubers have rotted
We had a beautiful pink, large double-headed peony and have had it for several years and it has bloomed without fail every year. But this year not one shoot came up, and upon checking the plant, we found that some of the tubers are squishy with oozing dark brown fluid. The only other flower in that particular flower bed are bluebells and daffodils which have bloomed as usual.
Peonies love their morning sun and afternoon shade. Nice loamy soil that is well draining. If the plants sat in soggy soil due to damp weather they may have suffered root rot.
Remove all the dead plant material as to not contaminate your other plantings.
Here are some links with more information.