It's always good to be hopeful, and any gamemaster who wants to save his players from certain doom can certainly invoke that. However, let's be realistic: even a full-on star system is mostly empty.
... while constrained to less than a month's fuel and a drive that can't exceed the speed of light. And as for rescuers jumping out and trying to find them ... same problem.
I understand that the chances are astronomically remote at best, but a ship's captain (by training) is going to attempt
something that represents the best chance (no matter how remote) of rescue. That needs to be factored into the discussion: what is a ship's captain going to
do in the situation? He is not simply going to accept the inevitable if he is at all worth his Master's Ticket.
That being said,
if the ship's captain finds himself at a distance of a lightyear or less from a system (or other body), the issue then becomes one of prolonging survival long enough to either reach that system/body or prolonging it until contact with that body can be established to secure rescue. Remember, the month of fuel you mentioned refers to its power plant duration
under normal load. A Captain is going to reduce his Power Plant output to bare minimum for life support if he is outside the maneuver distance to a nearby system/body. (There are rules in T5 for Reduced Power Plant Operations on p. 361-362, BTW: In
Quiet Mode the ship can Maintain Life Support [and little else] at 10% fuel consumption (= 10 months), and in
Long Term Mode the ship can run at 1% fuel consumption (= 100 months) and do little more than maintain its environment
without life support [you would have to determine just how much power Low Berths require, and possibly tweak the power plant low-consumption output to accommodate it]).
A ship could ... transmit a signal with its location/timestamp and velocity & acceleration vectors, and projected fuel reserves in a Signal GK toward the destination star-system, thus allowing the destination-system to get a fix on the current position of the ship.
Any starship should be able to determine all of the above parameters with precision. This is a prerequisite to its ability to astrogate in both Normal Space and for plotting J-Space Jumps.
1) If its location/timestamp can be determined (and its velocity vector will be the same one that it had prior to the initial Jump), and
2) Any acceleration vectors the ship makes after emerging from Jump are included in the aforementioned distress signal, and
3) The precise bearing of the distress signal is picked up by a receiving station in the targeted system (which it will be if it is picked up at all), then:
It should not be a problem for a rescue mission to locate the ship with a reasonable degree of precision, as all of the above parameters should allow a calculation of a fairly precise location of the vessel by anyone receiving the distress signal (the math is fairly trivial - a simple "ballistic" trajectory). The rescue ship would not need months-worth of search time.
The issue would be whether or not the ship could generate a signal strong enough to be picked up in the target system, and whether or not the ship power-plant on low-power fuel consumption mode could hold out for the time it took for the signal to be received, plus one week for the rescue vessel to make the Jump.
All of the above being said, perhaps the real issue should be that instead of
lifeboats/pods, regulations for ships should require enough
Emergency Low Berths for all crew and passengers (whether aboard ship or aboard Lifepod(s)). Some ships would carry Emergency Low Berths aboard, others would free up internal ship volume by carrying lifepods with Emergency Low Berths installed (that would not have to be launched from the ship unless absolutely necessary).
Hal & Whipsnade have already discussed this proposition above to some degree.