Offer letter and COS start date

[shipras]

Hello,

I've a query regarding a rather strange situation I might be in. I'm offered a job in a new company on Tier 2. As I'm already in UK the cos is going to be unrestricted. My question is:

1. Does the company's offer letter start date and the Unrestricted COS date need to be the same?
2. Also as I'm planning to go to my home country after leaving my present company and before joining the new one. Do I stand a risk in that case? I will be having my new tier 2 visa by then but I'm planning to request them a later start date instead. I'm totally confused and need some advice to work around this.

Thanks in advance.

Regards,
Shipra