When you are using old quizzes, first view the quiz by clicking on the title. Then in the right side menu you will see moderate options, but the options do not include reopening the current attempt. When I have had cause to reopen a student's current attempt of an old, I have had to create an extra quiz that is not counted in the final grade (I use weighted assignment groups and put this extra quiz in a zero percent group) I include only the questions they did not yet answer, and copy the beginning of any essay question they did not finish into the question. This is something I only do in very rare circumstances, and I do not think it is appropriate when you are having this problem with the whole class.
When I use timed old quizzes, even that only allow one attempt, my students are able to start and stop the quiz while the timer runs out. It auto submits at either the end of the timer or the available until date or due date (if those happen first). (Be careful that you have not set the time on those dates to the end of your in-person class. Set the dates and times based on when the quiz is to be turned in.) i don't expect the behavior to change for untimed quizzes, and so I would try something at the beginning of your class. Have everyone type their name in the first question of your quiz (or pick any random answer if it's not essay/fill-in-the-blank.) Then have them click on the course homepage without clicking submit. They will have to say OK to a warning message that they are leaving the quiz. Then have them open the quiz again while you are there watching. Based on my experience with my students the quiz should open in the current attempt. In fact the button that starts the quiz will now say resume. Your students may be hesitating to skip clicking submit, and clicking submit concludes your attempt.
