LDO with low-voltage cutoff?
I have never seen ready-made ICs with such a feature.

There are, however, ICs that have a shutdown (or enable) input that might be used for such a feature when you add an external comparator and/or reference.

You might also want to consider building your own LDO, using a PMOS (or pnp) pass transistor, a reference  (LT1431, LM4121-ADJ, LM4051-ADJ or even TL431 come to mind), some discrete components and some sort of 2nd comparator for the under-voltage lock out.

Take care about the regulator's stability (ESR of output capacitor must neither be too small nor too large, cf. "Tunnel of Death"). These links are helpful:

Short and good Application Note by NSC

A paper that offers some really good theroetical background

An entire thesis by the same author as the paper, also a good read

Building your own LDO has the disadvantage that you don't get features like thermal shutdown or short-circuit protection without additional effort, but it offers a great deal of flexibility (and it's fun).