Mushrooms are the "fruiting" structure of the fungus below the surface of the lawn, shrub bed and around the cut stumps of our many ash trees that have been removed. It will not matter if the stump was ground out or not. Fungi are decay organisms, feeding on dead organic matter. Without these fungi, the world would look a lot different. When you see mushrooms dotting the lawn, the fungi are typically feeding on the dead decaying naturally occurring thatch layer. This can happen with the weather we have been having and when a new sodded lawn is being overwatered for example.
There are several kinds of mushrooms and related fungi that can be seen in landscape beds that have been mulched. Good quality landscape mulches are ground up bark and lessor quality mulches also contain additional parts from a tree that will decay over time as well. These mushrooms can be very visual in appearance, having unique forms and colors. In a mulched landscape bed, the mulch will settle and create a good environment for fungi to grow when the conditions are right. Using a hard garden rake or 4 tined diggers to loosen and move the mulch around a bit will deter fungi from establishing and reduce the mushroom show.
If there has been an ash tree removed or other plants like a large shrub, the crown of the tree or shrub will start to decay and mushrooms room will appear around the base of the stump. It will take many years for the stump to finally be consumed. Since the Emerald Ash Borer has been around already for several years, another interesting decay phenomenon has begun to show up in the lawns. While the expectation of the stump rotting is expected, those roots radiating out from the stump are going to rot as well. Mushrooms are now showing up as linear lines, following the rotting roots in the soil from the stump outward. Later on as the roots are completely decayed, the lawn will become uneven as the soil settles and when walking over the lawn, you may actually "fall in". There is nothing you can do to prevent the decay process. Keeping the stump wet may speed the process up while covering the stump with soil will keep it from drying out and cooler, conditions that favor fungal growth.
If you have pets, do not let them eat any mushrooms. Reactions could be as simple as an upset stomach to nervous system issues with visits to the veterinarian.