Just to add for anyone who doesn’t know, the US astronauts do have a system they can use for self rescue. It can’t be used with the Russian Orlan suits though.

Hopefully this piece of kit which they carry with them on every space walk could get them back to the ISS in an emergency. Simplified Aid For EVA Rescue

Suited for spacewalking

It’s not got quite as much fuel as the MMU (which is no longer in use). Instead of 11.8 kilograms of nitrogen, it’s only got 1.4 kg which is enough for a delta v of 3.05 meters per second, or about 6/8 miles per hour - equivalent to a fast jog.

However, that should be enough to get back to the ISS after an accident that leaves them drifting in space at a moderate speed away from it. Never been used in an emergency though it has been tested in controlled conditions in space. One of the most useful features is that it can automatically stop the astronaut from tumbling. This would be very hard to do yourself, to do little nudges this way and that while tumbling over some random axis, to stop yourself from tumbling.

This is the last time it was tested:

See also Robert Frost's answer to If an ISS astronaut was disengaged from the station during a spacewalk, would we be able to recover him?

and Robert Frost's answer to How do the Russian EVA space suits on the ISS compare with the American ones?

WHAT ABOUT COMING BACK TO THE ISS?

If they drift away from the ISS, then the astronaut ends in an orbit similar to that of the ISS. If they drift away directly towards or away from Earth, the orbit will be the same period as the ISS, and in theory they should come back to the ISS half an orbit later, cross it and then end up going in the opposite direction, then back to where they started a full orbit later.

If they drift sideways relative to Earth - then they go into an orbit at a slightly different inclination, and the result is similar. The orbit has the same semi-major axis - so the exact same period. Same if they head off in any direction in the plane perpendicular to the direction of travel around the Earth.

That’s in theory. In practice, they would also have a different amount of drag in the very thin atmosphere up there, so will spiral slightly towards the Earth too compared to the ISS.

However chances are they go off in some random direction, not exactly in that convenient plane.

Worst case is that they drift away in the direction of travel around the Earth, or the opposite to the direction of travel.

If they do that they get further and further ahead or further and further behind rather quickly. Suppose they travel away at 2 m / sec, then every minute they will end up 120 meters further away. Every time the ISS orbits the Earth every 92 minutes, the astronaut gets an extra 11 kilometers ahead of it or behind it every orbit, and they get further away by 5.5 kilometers away after half an orbit.

So, the most likely scenario is that they miss the position from which they left the ISS originally by kilometers. To hit it they have to get thrown away from the ISS rather exactly in the plane perpendicular to its motion around the Earth.

Even traveling at quite a slow relative pace, the astronaut soon gets far from the ISS. This deployment of an old Russian spacesuit as a “suitsat” shows how it goes:

And so long as they throw it at least somewhat forward or backwards relative to the ISS’s orbit there is no risk of it hitting the ISS. It was thrown within the “cone of safety” to ensure no recontact with the ISS.

A typical space walk lasts for several hours List of International Space Station spacewalks - Wikipedia. So - if they got thrown off the ISS early in the space walk, there is some chance of them getting back to the ISS, would come past it several times, at a distance of a few kilometers - that’s where the question arises, whether you could do anything with the Soyuz TMA or the robotic arm.