  We study quench dynamics in a t-V chain of spinless fermions (equivalent to
the spin-1/2 Heisenberg chain) with strong potential disorder. For this
prototypical model of many-body localization we have recently argued that --
contrary to the established picture -- particles do not become fully localized.
Here we summarize and expand on our previous results for various entanglement
measures such as the number and the Hartley number entropy. We investigate, in
particular, possible alternative interpretations of our numerical data. We find
that none of these alternative interpretations appears to hold and, in the
process, discover further strong evidence for the absence of localization.
Furthermore, we obtain more insights into the entanglement dynamics and the
particle fluctuations by comparing with non-interacting systems where we derive
several strict bounds. We find that renormalized versions of these bounds also
hold in the interacting case where they provide support for numerically
discovered scaling relations between number and entanglement entropies.
