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).
The LM2596 is probably a bit better than what you think. If you look at figure 8 in the data sheet: -
It tells you that for a 1A load (at 25ºC) the drop-out is about 0.9V. Also note that the output is now just slightly out of regulation (Vout = Vreg - 50mV).
If you are running less than 1A this figure will improve.
However, take note of figure 11: -
It is telling you that at 25ºC the minimum operating supply voltage is about 3.6V (and this id for producing a miserly 1.23V on the output).
There are better devices than this I suspect and you need to consider what your maximum load current is when selecting one.
The LP2950 is a linear regulator and if you look at figure 10 it tells you that for a 50 ohm load and 4V inputted you will get about 3.6V coming out. Also look at figure 12 because this gives a different viewpoint in terms of output current.
Best Answer
They are quite similar.
I hope you're familiar how a LDO regulator works, so I don't have to explain that here. Remember that a normal LDO consists of a voltage reference, an error amplifier and a pass element (transistor).
A voltage tracker is the same except that it does not contain the voltage reference. Instead you supply the reference voltage externally.
You can think about them as voltage followers with built-in goodies like overcurrent, temperature and short circuit protection.
And to answer the possible follow-up question right away: "Why do I want a voltage tracker instead of just using a cheap opamp as a voltage follower": A voltage tracker has no problems driving capacitive loads which you need in most voltage supply applications. Opamps on the other hand rarely tolerate more than a few hundret picofarads at their output. They aren't suitable to supply voltage for micro-controllers due to the lack to drive bypass capacitors for example. Voltage trackers on the other hand are.