This is a question that is often asked and does not have a clear or obvious answer. Everyone is looking for easy and natural ways to treat any condition and a plantar plate injury is no exception. The plantar plate is a strong ligament under the joints in the forefoot that can sometimes get strained due to overuse. Occasionally a small tear develops in that plantar plate ligament.
The typical symptom is pain under the ball of the foot that starts as an ache that gets progressively worse. It is typically much more painful on palpation or poking it. Also the affected toe does tend to be in a more dorsiflexed position.
So, can it heal by itself?
A common treatment (strapping or taping) holds the toe in a plantarflexed position so that it can heal. Is that healing on its own? It could be considered that or is the taping seen as a treatment so that its not healing on its own? Or is this just semantics?
In reality they probably can not heal on there own. They can healing with the strapping and maybe a stiffer soled shoe given time. If those types of treatments do not help, then a surgical repair of the tear in the plantar plate is probably warranted.