As far as I'm aware, the transition window exists to protect coaches from financial losses. Aliona Kostornaia will compete officially as a member of Sambo 70 as a protection to Eteri. So whatever awards Aliona wins this season, Eteri will still receive the same cut she always did, even if she's not actually responsible for Kostornaia. The same would be the reverse, if Aliona had switched from Plushenko to Eteri, then Plushenko would receive all the funding. This is why Plushenko mentioned "we will make sure we handle her funding" because Eteri technically still gets all the national team funding for Aliona.
As for whether or not a coach can kick out a member of a national team outside of the transition window, I do not know. My immediate guess would be... no, unless there was some exemption and they also forfeited funding. But do not quote me on this, that's just my conjecture given how it works the other way around.
Rusfed gives 2 types of funding to the athletes
1.personal funding AKA monthly stipend- Obviously differs if the athlete is in the main team or reserve team. doesn't matter if she switch coaches, injured or not training. Funding only stops when athlete gets booted off the national team or officially retire. Officially retire means they have to file the paper because it also legally stops the Rusfed to make money off of the athlete. So no matter what Kostarnaya is and will still get her monthly stipend As long as she remains a national team member.
2. Club funding- Coaches doesnt get an actual funding from the Rusfed. Rusfed gives the money to the club and the club will disperse it to coaches/trainers etc or whatever arrangements they have. Eteri doesnt own Sambo. She is just one of their many coaches. So doesnt exclusively pocket An athlete’s club funding.
Also the only events Rusfed officially fund the competition/training expenses of a coach/athlete are European/worlds/ Olympics. The rest its a club funding.