Do dead cells always contain no nucleus?
If you're looking at cause of death by standard apoptosis, to initiate the process, cytochrome c will be released from the mitochondria, bind with apaf-1, and undergo a structural change resulting in what looks like a biochemical ninja star (figure 4). This will activate caspase-9 which will activate other executor caspases, eventually creating an avalanche of protein-degrading enzymes that will leave the structure and organelles of the cell looking like paper mache. Regarding the nucleus, the complexes of enzymes meant to maintain dna integrity and structure will be degraded, the DNA's network influence on the cell will become largely inert, and the dna will be condensed and broken apart by nucleases. The membrane of the nucleus is full of proteins and ribosomes, and these will be degraded too. If you are looking to simply identify an inert nucleus by its skeleton, you may not have much success either - here are a few good images from a nice study showing the progressive destruction of a nuclear structure.