Firstly, you haven't specified whether the kids know
where their parents are. (They might have been kidnapped, or had an accident and be in hospital.) Of course, if they don't know, then they will almost certainly attempt to find out and this will have a large impact on the plot, so you may not want to go that way.
You could try looking at the flip side — why is the 20-year-old still living with his parents at all? For example, if it's because he's attending university in the same town, that gives him a good reason to stay put if the parents relocate, and they might just decide that to avoid too much upheaval it's easiest for all three kids to stay. So in that scenario, the reason for their absence could be as simple as a job opportunity in another town or country.
Another possibility — you may not like the above "running from the cops" idea, since if that were the case the cops would probably keep close watch on the house and might interfere — but they might be on the run from some other danger they don't want to involve their kids in, for instance a criminal gang they've gotten involved with who are threatening them.
It would help if you told us a bit more about the setting you're writing in, to be honest.