My sims birthday moves a day every time a day passes in the sims world

@Starlingthejay What direction is the birthday moving, later? So, they basically haven't aged? That's normal if your Sim is pregnant -- pregnant Sims don't age. A few in-game Sims are also "special" and set to immortal, so if you started playing as one of those, you might have hit an issue; I believe they all start as unhoused. The other in-game cause is that you've used Game Options to set the active household not to age.

Otherwise, MC Command Center can be used to set a specific Sim to be immortal. But you'd have had to do that deliberately. It's not a default.