Pretty much every record in epesi has full edit history attached to it.
Simply go to Tasks, in Filter (to the top-right) enable checkbox "Display closed tasks" and find the tasks that you're interested in. "View" that task and on the top-right corner you can see small "clock" icon. Click to to see the full history: who, when and what was changed.
if it turns out that those tasks are not closed but in fact deleted - you will need admin privileges. Head to administration panel, "Records Sets", select "Task" at the top and find the one Task that you want to look up. You can jump to edit history of that record straight away ("clock" icon is also there next to the "view" action) or you can view the record and then check edit history.
This should solve all problems as to who did what and when. 🙂 (save for some administrator actions and assuming no access to Database, of course 😉)
EDIT:
This is the intended behavior, the same as with Tickets. Closed task/ticket should vanish in the annals of history and we don't want to encourage re-opening them as default action. As you pointed out - that option is still there if someone really needs it, by editing the record.
If you want to have the final word as to what gets closed and what stays open - tickets module is just for that. Only ticket owner can close the ticket, those assigned to it can set the status to resolved topmost.
Tasks are more for small-time or personal jobs to perform, it was not designed to provide the kind of management and control that we included in Tickets.
Kind regards,
Arek