On the boat from Shiganshina, Mikasa realized she was homeless. Again. Eren was still shell-shocked at seeing his mother's death and too busy swearing vengeance at the invading titans. Armin and his grandfather seemed to have the same thoughts as his grandfather tried to inconspicuously rummage through his pockets. Between Mikasa and the two Arlerts, they didn't have much. Judging by nearby ship passengers, they didn't have much either.
There were also some obvious glances towards the three children's direction. Eyes roamed over Mikasa's exotic looks, Armin's somewhat feminine features and Eren's tear-stained face. Mikasa left Eren to the care of the Arlerts and went to 'ask for food'. She didn't find any, but nobody said anything when a couple of passengers disappeared on the way to Rose. Grandpa Arlert's wallet did get suspiciously heavier though.
News on Maria's fall only arrived with the ship, so they got lodging on pure luck. Armin knew that charity from the government won't come forever. Even Mikasa's contribution, they wouldn't be able to survive. He looks at his journal and pencil, the only thing he had on him from Shiganshina. There were only a few pages filled in his neatest handwriting and all of it was about the outside world. Now, it would be his weapon to survive. Armin turned to the next blank page and wrote down the names of the two Garrison bastards who kicked his best friend.
Their permanent lodging turned out to be next to a brothel. The former prostitute didn't blink an eye at charging an exorbitant price for one room to one old man and three children. Even Eren's best 'lost in the woods' act didn't help that much. Still, it meant that they had somewhere somewhat safe to sleep - even if the walls were thin and the roof occasionally leaked. He didn't like the way the old lady eyed Mikasa and Armin either. Armin's grandpa wasn't doing too well either. The loss of his son and daughter-in-law combined with his age left him with a nasty flu. The incoming winter wasn't helping either. Being a doctor's son, Eren knew a couple of tricks to dulling pain, keeping health, secretly and slowly poisoning the abusive landlord next door... For some reason, Armin was always tired in the morning. Maybe it was too noisy for him to sleep? Well, all the more reason to keep poisoning the landlord. The girls next door seemed to have a better time when he's stuck in the toilet.
It was lucky for Eren, Armin and Mikasa, that the first slaver out to break into their new home did so when Grandpa Arlert was out trying to look for a job. In other words, it saved Grandpa Arlert a heart attack from watching an eleven year old questioning a thirty-something man, another kid torturing said man until he answered (being a doctor's son meant knowing about pressure points and other sensitive areas), another kid murdering the man in cold blood and the three teaming up to hide the body.