Rhombics and other traveling wave antennas may use a resistor to terminate the ends. Another example would be a size reduction of a circularly polarized multi-arm antenna, surrounded by a shorting ring. The ams would either be connected directly to the shorting ring or left open but both approaches have their disadvantages. The optimal solution turns out to be using smd resistors to terminate the ams to the shorting ring. By doing that you can extend the lower frequency coverage of an antenna of a given size by around 25% as well as smooth out the irregularities in the frequency response (its a broadband antenna)
Another application for loss which clearly has practical benefits are cavity backed antennas where the cavity is filled with some RF absorbent material.
In that application the goal is to completely null out any reflected signals from below. Most of the spiral type circularly polarized antennas are inherently bidirectional, but for a space to ground application if you are on the ground you just want one direction.
There are a number of ways to do it, one is something called a choke ring which is a quite frequency selective trap for reflections. (it looks a bit like a circular cake mold) Another is a cavity which can be made to be fairly broadband using resistive materials. That can be built inside of a can that forms the back side of your spiral. Its popular in military broadband antennas too.
Also, it seems some people build intentionally lossy antennas (such as verticals with lossy baluns) They clearly have their fans, because of the ease of tuning. A lot of people seem happy to accept a fairly lossy antenna (or balun) because it gives them perceived benefits in ease of tuning. (My memory may be fuzzy on this, there may be other reasons, less need for radials, or some such)