Was lucky enough to have the company I was recruited for help me by having their name on the rental agreement, covering any expenses the owner might have if I thrashed the place, didn't pay rent, etc. Ended up finding a place for 13.000SEK/month on the outskirts of Stockholm, at the very last subway stop.
For most of the employees starting at the same time as me, most of their rental agreements were only valid for a year or so (and the owner could kick renters out pretty much at any time), forcing people to go and find other apartments, which is not easy when the employer no longer offers support with the contract.
One colleague of mine found that his response rate was extremely low on his bot that automatically applied for an apartment, which matched his criteria, as soon as it came up online. He suspected his non Swedish sounding name was a factor, so he changed the name in the message to something Swedish-y ("Sven Karlsson" or smth. like that) and instantly the response rate rose dramatically. As a foreigner, not having anyting on your Swedish credit report doesn't help either.