Can it be someone on TPS? Answer: no.
Can it be someone living permanently abroad? Answer: no.
Under 8 CFR 213a.2(c)(1)(i)
(i) General. A sponsor must be:
(A) At least 18 years of age;
(B) Domiciled in the United States or any territory or possession of the United States; and
(C)
(1) A citizen or an alien lawfully admitted for permanent residence in the case described in paragraph (a)(2)(i) of this section; or
(2) A citizen or national or an alien lawfully admitted for permanent residence if the individual is a substitute sponsor or joint sponsor.
See more at https://www.ecfr.gov/current/title-8/chapter-I/subchapter-B/part-213a#p-213a.2(c)(1)(i)
Affidavit of Support laws could be found here.