The HR expert's most intelligent negotiation in a job offer: "I always advise my clients to do that."

Many individuals anticipate negotiating the salary of a new job offer, in addition to the numerous other advantages that are available.

But have you ever thought about negotiating your exit from the company?

Tessa White, a career coach with 20 years of HR experience and founder of The Job Doctor, was able to weather a layoff earlier in her career.

White tells CNBC Make It that the smartest thing he ever did was pre-negotiate his severance agreement.

At the time, White was being considered for the head of HR role at UnitedHealth Group.

She didn't expect the company to change their severance policy, but as a single parent with three children, she wanted to ensure protection from uncertainties if she joined the company.

Negotiating your severance is the best time to "when they love you at the company" and want to hire you.

Her pre-negotiated severance paid off

White claims that negotiating her severance early on would have allowed her to assure her new boss of her commitment to the job while also securing her future career and financial stability.

I am confident in my abilities and believe I will excel in the role. I do not require severance if my performance is terminated.

She argued for more financial stability before transitioning to a new company. She explained, "I'm taking a risk on something that's currently stable for me to join a new company, and I want to ensure that I have the security to land on my feet if any unforeseen events occur, such as a merger, acquisition, or shift in business priorities."

The company agreed to increase her severance pay from two months to four if she was let go for reasons unrelated to her performance.

Several years later, the company underwent a change in ownership and relocated its headquarters. As a result, White was asked to relocate or lose her job with severance.

I knew I could care for my family and land on my feet because I had secured extra severance coverage, which made all of the panic go away when I heard the big changes that were ahead.

She advises others to do that frequently, stating, "I always recommend that to my clients," and "every time a client has requested it, they've received it."

What you can negotiate in a severance agreement

Negotiating certain terms of severance agreements may be possible after a layoff is initiated, but flexibility is not always available. Companies typically have a policy regarding the amount of severance pay based on an employee's years of service. However, it may be worthwhile to request longer coverage if you are a high-performing employee or in a senior role.

You can choose to receive severance pay in either a lump sum or installments, and negotiate for the payment method that best suits your financial needs.

White suggests that you may have more flexibility in negotiating the number of months or amount of coverage the company will provide through COBRA.

Unless your termination poses a risk to the company and could lead to a lawsuit, other post-layoff negotiations are less likely.

It is easier to have a severance discussion before a layoff occurs, according to White, and "difficult on the back-end, if not impossible."

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