[dudul]

Isn't there a 10 year limit as well though? Especially for this case where someone serves as president without being elected?

That being said, I'm not sure either if the restriction in the parent exists.

Edit: a reference I found afterwards https://en.wikipedia.org/wiki/Term_of_office#Federal

[GavinMcG]

Not exactly. The 22nd Amendment would prohibit the second election of someone who had served for more than two years without having been elected.

For example, if Gerald Ford had been elected president after he finished Nixon's term, he would be ineligible to be elected a second time, since he initially served for a little over two years and five months.

That doesn't change the fact that the 22nd Amendment only restricts the election of a president. If someone has already served in the office for ten years, they could still be the VP who upon whom the presidency devolves, because there is no constitutional restriction on such eligibility.