Ranks are distributed (probably) normally based on everyone's ELO, not just yours.
While you were asleep, other people gained ELO, changing the ELO distribution, and hence decreasing your rank (this could also increase it).
When you won four games in a row, others won games and gained ELO as well, so the distribution didn't change. That last one apparently put you over the threshold.
When you win or lose, your rank doesn't go up or down, no. What happens is that your ELO (or glicko, or whatever they're using under the hood) goes up or down relatively based on the distribution of ELOs in your match. That's a hidden number that you have no way of seeing. Your ELO is not your rank, but they're related.
Usually they do it in such a way that you gain more ELO for 'unexpected' wins and less ELO for 'expected wins' (e.g. if your team was better to begin with they barely gain ELO, if at all). That could account for matches 'not doing anything'. In most systems, if one team has higher ELO than the other team across the board, then if the team with higher ELO winning usually does less to everyone's ELOs (if anything at all). If the team with less ELO wins, they gain a lot and the other team loses a lot.
Afterwards, ranks are based on ALL ELOs of ALL players. So, if you're in the lowest (as an example) 9% of ELOs, you get moved to Initiate. If you're in the highest 9%, you're in Eternus, same for everything in between (though it's probably a normal distribution so not exactly 9%). But which bracket you're in depends not just on your own ELO, but also on everyone else's.
So yes, what other people are doing while you're asleep can absolutely affect your rank.
