For example: a system with a 0.2 solar mass white dwarf orbiting a 0.25 solar mass red dwarf. Does the red dwarf steals mass from the white dwarf or vice versa.
$\begingroup$ This would depend on how close they were $\endgroup$– adrianmcmenaminSep 3, 2017 at 17:02
If they are close enough to exchange mass, the Red dwarf will always lose mass to the white dwarf. That doesn't mean there won't be some exchange going back the other way, but the white dwarf will always win the exchange rate and it won't even be close. It makes no difference whether it's heavier or lighter. What matters primarily, is how tightly held it's outer mass is to each star and how strong the tidal forces are.
The white dwarf's mass is very tightly bound to it by gravity and being so small, it's not going to experience strong tidal variation. The red dwarf's outer layers are far less gravitationally bound to it, and being much larger, it experiences greater tidal bulging.
How much mass is exchanged would depend on how close they are, but around any star, and if they are close enough, the white dwarf will always steal mass from the main sequence star.
A curious thing happens with main sequence stars. As their mass goes up, their surface gravity goes down. A star with 0.25 times the mass of our sun, extrapolating from this chart would have a radius about 32-33% of our Sun, and being 1/3rd the size, using the inverse square rule, it's surface gravity would be about 9/4ths or 2.25 times the gravity on the surface of our sun - roughly speaking. There would be other factors like rotation rate and solar storms, and, as mentioned above, how close they are, but there's no way that a main sequence star of any size could steal more mass than it gives up from a densely packed White dwarf.