Stuck Without a Resignation Letter: How Can I Move On to My New Job?

MNemployee
Hi everyone, I am caught in a very tough situation. Since March 2020, when this COVID pandemic situation started, my work was called off. After some relaxation in the lockdown, they started working, but I didn't get any words from them. I tried many times but didn't get a reply. So, I decided to resign from there and started to look for a new opportunity. Now, I have found a suitable position where I can start my work, but my employer is not acknowledging my resignation. I did send my resignation letter twice; it's already been 30 days today, but I am not getting any reply on that. What should I do now? I am not getting a resignation letter. The new employer is asking for the same upon accepting the job.

Background about the employer where I worked

It's a proprietorship firm. They don't provide any kind of letter of intent such as joining/appointment letter/salary slip. They do not have any kinds of rules for resigning/exiting.
MNemployee
Anyone, can you please share what to include in a letter if I am asked for a self-declaration? Alternatively, can I send the letter in this way: "If not acknowledged in 3 days, then it will be treated as resignation accepted"?
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