Is a power adapter with a loose prong safe to use?
There are several risks here. The first three I can think of are:


If the prong is pushed too far into the case it may touch other parts causing a short circuit, possibly putting line voltage on the output. Ideally it would be designed internally to prevent this possibility, but you don't know.
If the prong is also able to be pulled out, then unplugging the adapter could leave the prong in the outlet, resulting in live exposed metal.
Plugging it in might work but make poor contact, resulting in overheating at the plug (probably not) or intermittent operation.


It is unlikely that the adapter can be repaired adequately. Instead, purchase a replacement of the same voltage, current, polarity, and output plug type.