cat, I take it that's what she meant too. It's just annoying to me because the vast majority of immigrants don't have any recourse to public funds. Those who do, tend to be asylum seekers, people who fled at risk of their lives and didn't choose to come here.
Changing immigration status is what you do when you apply to, well, change your status under UK law. It's pretty simple despite the jargon. Basically, you might start out (like my DH) as an overseas student, or as a short-term migrant (ie., someone with temporary leave to work here). To get both of those visa statuses, you have to demonstrate you fit the criteria for them - you won't be allowed to access public funds, naturally, and you will have to prove you can support yourself and you are good enough at what you do to be a benefit to UK economy, not a detriment.
After that, you might apply to change your immigrant status - eg., my DH was on a student visa then applied for temporary leave to remain under a work visa, when he got a job. He had to prove (again) that he had enough money to support himself.
Recently he had to apply a second time for another stint of temporary leave to remain, after we got married. Of course, the fact we were married was irrelevant - if he hadn't been able to support himself, and with a good job, he would have been deported.
He will eventually be able to apply for permanent leave to remain, assuming he stays able to support himself and in a sufficently high-earning job. He'll have to go through yet another process to prove this. Each time, of course, they are mostly confirming the same old news they knew before.
One day, we hope, he might get citizenship.