I learned this the hard way, and now insist upon a contract before agreeing to move to a company (i.e. I dont tell my previous job or give a start date until I see a contract).
"Signed" isn't what you think it is. You can sign the offer letter, and possibly a couple other things, but most companies will also have more documents that you must sign on your first day of employment, and won't give them to you before then.
Interesting. That's not how it works in Australia at all.
Here, salary expectations are given in the first screening call. If they can't meet the expectation or you won't be happy with their lower offer things end there.
Interviews / code tests happen.
Offer comes over phone or email. This includes salary.
There is no signature at this stage and nothing is set in stone, its just an offer. If you accept the offer a contract is drawn up. Still nothing is certain.
Changes to the contract can happen here.
Once both parties sign. That is when you're "signed".
This happens well before your start date, usually you would stipulate the start date in the contract, so if you need to give a month's notice to your employer your new contract with a start date from a month is signed before you even hand in your notice.
There is a 3 month trial period on all employment where they can walk without much repercussions, but this is more of a concession on your part because employment is very well protected.
Any weird IP bullshit or other conditions of employment that need signing would be in the contract you signed on for.
They can't bait and switch like what you're discussing. Any NDA's are discussed up front and at least their existence is disclosed in the contract giving you a chance to see them early.
Basically you can't put new conditions of employment on people after the fact, and if you did it wouldn't be valid in court anyway, contract law trumps contract content here no matter what.
Things don't have to work exactly like this, you might want to leverage the offer for a higher pay at your current job, counter offering is commonplace here but I wouldn't ever accept one. They'll be looking for your replacement as soon as you accept.
That hasn't been my experience in the US. When I joined, I signed everything along with the offer letter. Full 10-15 pages of contract. Nothing to sign on the first day.
So far, it hasn't been a problem.