With a demissionary cabinet parliament decides which issues are controversial, which bars the cabinet from drafting legislation concerning them.
A rump cabinet can take care of such issues but it does not have a majority in parliament and thus needs approval by opposition parties, which make it likely that the rump parliament will take great care dealing with controversial issues.
Generally the rump cabinet will only take care of going government concerns (as a caretaker cabinet) as well as preparing for elections.
For the formation of a rump cabinet the Monarch will appoint an informateur and later a formateur, just like with a regular cabinet formation after elections.
This article about politics in the Netherlands is a stub.