I've actually tried that cute "Strike out clauses from your employment agreement you don't like and sign THAT document" tactic with several past employers, and each of them pulled me aside my first or second day of work and gave me a stern and clear "Sign it unmodified or GTFO" talk. In my experience nothing in an employment contract is in any way negotiable. I don't even bother anymore--it's futile.
Either they're bluffing completely or you're extremely junior.
We often spend $10k-$30k on each new hire. If you make it through that pipeline and they try to strong-arm you on the first day... they're going to have a rough time.
I don't think they were bluffing but I was not going to roll the dice and find out. Not a junior level guy either. I think these places that actually let you negotiate your employment contract must be relatively few, very small companies, with one HR person and lawyer and a lot less formality.
EDIT: Also, to be cynical: $30k is nothing for many companies, and likely less than the benefit of having IP rights to everything an employee makes in their spare time.
If you are willing to lose your job, I applaud anyone who does this fight. But lots of people are not able to do the same fight.
What does work is demanding to see the employment contract before joining the company. They can present you with a different contract on day one, but contract law requires a meeting of minds, and if they snuck a new clause in without calling it out, there wasn't a meeting of minds.
Don't look for jobs when you're desperate. Look for jobs while you're happy and comfortable in your current position.
It's like investing. Don't buy while the market is going up. Buy after a crash. Buy when the deck is stacked in your favor.
I (mostly) only ever actively look for positions when I'm comfortable in my current position. If a new employer really wants me, they'll bend over backwards to get me. I recommend everyone do the same.
Sometimes you may not have that leverage. In those situations, absolutely take whatever job you have to take to keep your house and keep the electricity flowing. But don't stop looking for a better job.
You are literally the only person on the planet that is going to look out for your best interests. The difference beteween a 100,000 and a 110,000 salary over 30 years is freaking $300,000 (not even counting for investment potential). Maximize your career for yourself.
In my experience employment contracts are negotiable if and only if the negotiations are carried out BEFORE accepting the job.
Before responding to an offer, I've found it important to ask, "Please also send me a copy of the employee handbook and any employment agreements or other documents that I will be expected to sign on the first day of work."
I've done this ever since the time I quit one job, started another and then on the first day was presented with an HR packet full of "standard" forms to be signed.