There is not actually survivorship bias in the DJIA, because changes to its composition are not retroactive. If an index member goes bankrupt, it will absolutely bring the index level down substantially.
So you're correct in that bad performance by a firm in the DJIA will affect the index, however, really bad performance by a company will not be completely reflected in the index, only the first part of their decline. And that will be somewhat mitigated by the inclusion of their replacement, which is usually a growing company.