Heeding this advice would be much more generous than employers typically are, especially in an at-will employment environment. In my experience, employers give zero notice and provide zero assistance helping an employee find a replacement.
Perhaps I should add that this advice best (only?) applies if you're leaving a company in a sort of "natural parting of ways" kind of situation? Thanks for the feedback.
Regardless of the cause, an employer almost-always will require a separation agreement be signed as a requisite action for any amount of severance pay. This is entirely to the benefit of the employer.
Both sides get something from the agreement. Employer gets certainty. Employee gets certainty and some money.