Expired L permit and work contract

Visas, Permits, Passports and Naturalization
1
I am a non-EU national and I obtained my PhD degree here in Switzerland in August 2021. Then, I applied for L permit for job-seeking until the end of February. Unfortunately or fortunately, I got a job offer just one day before my permit expiration day. I contacted HR and consultant agency for foreign nationals to whether I can stay here after my permit expires and both of them told me not to leave the country to shorten the work permit application process.

However, I got a warning letter from the canton to extend my residence permit as soon as possible. I am a bit concerned now about my residence status.

1)Is it possible to stay in Switzerland after having a job offer and while waiting for the contract discussion?

2) Does overstaying affect my work permit application?

I would be very grateful if someone replies to my questions,

Thanks in advance

2
Welcome to the Forum.

If the canton has sent you a warning letter, do not ignore it. Overstaying your permit without permission could mean you do not get a new one and therefore do not get this new job. It could even see you banned from Switzerland and/or Shengen if the authorities wanted to be really strict.

As a non-EU, your employer has to go through a process to hire you that's a bit more complex. If it's a renewal then it should be straightforward since they already did it. If it's a new employer, you need to tell them to get in touch with the canton ASAP to ensure you can stay while they are processing.

3
You asked the company but you didn’t ask your cantonal immigration department - it’s their decision, not your companies.

4
Thanks for your messages.

It was my fault not to ask the cantonal immigration department. I went there today. I am told that I have to provide an official offer letter from my employer very urgently. If I can show my contract is under preparation, they will provide me with a temporary permit to stay in Switzerland at this stage.