Near the top of daf 81a, Abaye says 'de'Ba'in Alav mi'Sh'nei Tzedadim'. The Beis-Din can reply to the Yavam from either "side" of the claim that he doesn't want to bury the Shomeres Yavam.
Can the Yorshim outright refuse to be Yoresh, and through their refusal to inherit from the ba'al, also refuse the chiyuvim of the ba'al? A practical case might be where the ba'al's estate is worth 100 zuz and the debts are also 100 zuz. Are the yorshim entitled to say "I don't want to be involved at all and refuse their inheritence and the obligations that flow from the inheritence?, thereby escaping this obligation to bury the Shomeres Yavam?
Any heir's liability is limited to the amount which he inherited. Even the Yavam would never be liable to bury his brother's wife from his own funds.
The Gemara in Bava Basra (124a) says that a Bechor (firstborn son) may forego his double portion of the inheritance in order not to have to pay extra debts. It is unclear exactly what he gains by this. However, other heirs may not forego their inheritance, nor may the Bechor forego the portion he has coming to him as a non-Bechor. This is true of any d'Oraisa inheritance. As for rabbinic inheritance, one may forego it although it might be necessary to do so before the death of the benefactor (see Daf 83a).