Will you lose a job offer if you negotiate?

Losing an offer because you negotiated is uncommon when the request is polite, specific and reasonable, and many employers expect some negotiation. The risk goes up with ultimatums, several rounds of new demands, numbers you can't support, or reopening terms you already agreed to.

What keeps the offer safe

Say clearly that you're excited about the role
Make one specific request, not a list
Give one reason tied to the role or the market range
Stay warm if the answer is no, and ask what is possible

What raises the risk

"I won't accept below X" when you would
Claiming a competing offer you don't have
Going back with new demands after each answer
Negotiating pay set by a public scale or union contract

If they say no

Thank them, ask whether another term is flexible, and decide with the full package in front of you. A clear no is information, not a rejection of you.

Questions

Do employers expect candidates to negotiate?

Many do, and some build room into the first offer for exactly that reason.

Is it safer to negotiate by email?

Email lets you choose your words carefully and gives the employer something specific to take to approvers, which usually helps.