Stars don't "lose" their "main sequence", because it's not something a star can "have" in the first place.
Stars are more properly described as being "on" or "off" the "main sequence", and "sequence" isn't a good word for it anyway, because it implies that there is an actual sequence of events involved; in fact, the normal life sequence of a star has it going off the main "sequence".
It may help if you stop thinking of them as "main sequence" stars and start thinking of them as either dwarfs or type III stars.
This happens when a main sequence star uses up all of its fuel and swells. Next stage: Red Giant.
No. Red giants are not on the main sequence.
A red main sequence star would be a red dwarf or a branch red giant. To be on the main sequence, you have to have hydrogen nuclear fusion.
The sun is a main sequence star, so 1 AU.
Main-Sequence star
None of those is a main sequence star.
Sirius is not a single star but a binary star system consisting of a white main sequence star and a white dwarf.
The defining characteristic of a main sequence star burns hydrogen to helium in its core.
Most stars are on the main sequence; that includes red dwarves. Specifically, in this case, the closest known star - Proxima Centauri - is also the closest main-sequence star.
Algol is a blue main-sequence star in the constellation Perseus
When a star "goes off the main-sequence" it generally means the star has run out of hydrogen fuel and is beginning the post-main-sequence or its end of life phase. The main sequence of a star is the time where it is no longer just a proto-star but is burning hydrogen as a primary source of fuel.
Any star that it fusing hydrogen into helium is classed as a main sequence star.