They knew that they couldn’t retrieve her alive, so there was a euthanising device of some sort aboard, as a humane measure. I believe that it was an IV inserted prior to launch, but I could be mistaken.
This site says that Laika died when the batteries of the life support system ran out. However, another site says:
The second source sounds more authoritative, though I’m pretty sure it got Laika’s gender wrong.
Anyway, the capsule reentered the atmosphere and burned up half a year later. In “low earth orbit,” which includes all manned flights except the Apollos, there is still some residual air which slows down the spacecraft over time. Everything comes down after a few years unless you fire rockets to rais the orbit from time to time.