By definition, when a death is diagnosed as an instance of SIDS, the actual cause of death is not known. (If the cause is known or is determined by autopsy, the diagnosis is not SIDS.) Thus there can be no proof that the bassinet was the cause, or even a contributing factor, in the death, and therefore the seller of the bassinet should have no liability.
If there was some other cause of death that was due to the condition of the bassinet, there could possibly be liability. For example, say the bassinet broke suddenly, causing the baby to fall and death resulted. But here I think ther could be liability only if the seller knew (or suspected) that the bassinet was in an unsafe condition, or if a reasonable person in the seller's position would have known or suspected this, or possibly if the seller made knowingly false statements about the condition which made the bassinet seem safer than it in fact was. None of these matches the situation described in the question.
However, in many jurisdictions there are laws specifically forbidding the sale of used mattresses, adult or infant, regardless of their detailed condition or how they are described. In such a jurisdiction the seller could not lawfully include the mattress as part of the sale. With a new mattress it would be even harder to link the seller to any SIDS case, as any risk factor from an overly-soft mattress would not be the seller's responsibility.