You might feel that both of your remote jobs are safe, since it's not illegal to have two remote jobs at once. However, that doesn't mean that your choice to work for two employers remotely won't result in you being fired from one or both positions. For those considering working two jobs in short periods between jobs, that should be fine. There is a small unknown risk of how your next employer would perceive your hustle and bustle, assuming that you had to include both employers in your resume, or else there would be too big a gap.
The good news is that there are many explanations, such as a leave of absence for reasons of education or military service. For all we know, he could have an extended severance payment that would keep him on the payroll. The list of excuses is endless. If you're pressured, you can tell the truth: you wanted to tie up some loose ends at your old job before you quit and there was no conflict of interest.
In the end, I don't think your next employer would mind, unless you were aiming for a higher position on the career ladder close to top management. The golden rule, first of all, is not to talk about having two remote jobs. Yes, even family members outside your home. If you can't keep that secret yourself, how do you expect others who have nothing to do with the game to do it? This is for your own protection.
Most people who have two jobs come from connections that share the same network. Woods, who is a full-time account manager at a software company, also sells furniture for a retailer. He said that working remotely for both jobs allows him to avoid being caught and that was only possible during the pandemic.