A Nachmieter takes over a tenancy when the current tenant leaves for good. You will see Nachmieter gesucht in the same groups as the sublets, and it is a different and usually better proposition: rather than borrowing a flat for three months, you are being handed a real Berlin lease.
The reason people advertise for one at all is notice periods. A tenant who wants out sooner than their Kündigungsfrist allows can often leave early if they present the landlord with an acceptable replacement, so finding you solves their problem. It is in both sides' interest, and it is why these posts are worth watching for even when you are only looking for something short.
The catch is that the landlord decides, not the departing tenant, and the landlord will run the normal checks: proof of income, usually a SCHUFA report, sometimes a Mietschuldenfreiheitsbescheinigung from your previous landlord. Someone three weeks into their first Berlin job will struggle. Someone with a permanent contract and a payslip has a real chance at a flat that would never have reached the open market. Ask the departing tenant what the landlord will want before you apply.
Beware one variant: a “Nachmieter” post that wants a large Ablöse for the fitted kitchen and the furniture. That can be perfectly legitimate (see that entry), but it is also where the money is, so it is where the overcharging happens.