The right of the alien (also the government) to sue for enforcement of the terms of the contract is statutorily guaranteed under 8 USC 1183a, it is open to the alien, and there is no express provision for waiving that right. However, there is case law. In Blaine v. Herrell, the case involving waiver of legal support rights via a premarital agreement, and whether an I-864 affidavit nullifies the right to waive such rights. The court found that it does not – you can waive such rights.
It is however, a basic principle of contract law that a party may
waive legal rights and this principle is applicablehere. See, e.g.,
Navellier v. Sletten, 262 F.3d 923, 940 (9th Cir. 2001) (upholding a
contractual release explaining that “there are no genuine issues of
material fact indicating that the challenged release was either
procedurally or substantively unconscionable. As the district court
noted, Sletten freely chose to waive his legal rights in order to
preserve the stability of the Fund.”) In this case, Plaintiff (the
sponsored immigrant) signed a contract directly with Defendant, the
Pre-Marital Agreement, in which he voluntarily chose to waive his
right to any support from Defendant. The Pre-Marital Agreement was
entered into a year prior to Defendant’s signature of the Form I-864.
The court concluded
the Court finds that Plaintiff has waived his right to enforce the
Form I-864 by entering into the Pre-Marital Agreement. Plaintiff
cannot escape his own voluntary choice to enter into the Pre-Marital
Agreement in order to marry Defendant.
If applicable (and it's not guaranteed that it would be), that could remove the parent from the set of parties that could enforce the contract – various governments could still. In addition, by adding the element of fraudulent intent, you would still be subject to numerous penalties for perjury and so on, and the agreement you made with the parent would be itself found to be invalid (in the above case, the prenup was legitimate, not a scheme to gain a green card).
This article discusses some of the legal theories involves in waiving I-864 rights, but the same author elsewhere recognizes that "The majority of courts to consider waivers of I-864 rights have found such agreements to be unenforceable, though the reasons for this holding are misguided".
As for the possibility of a person waiving their right to receive public support, that would not be enforceable: basically, "the public" is not and cannot be a party to an agreement. For instance, if the alien were to claim a statutory right to support in Idaho under Idaho law, Idaho cannot argue "The alien entered into an agreement with Citizen Z to never claim this right". The scope of any possible waiver would be limited to claims by the contracting parties. Welfare is generally an unwaivable right.