Someone is indeed in a fine mess:
1. A work permit is no longer valid after you leave the sponsoring employer be it through resignation, being fired etc. Subsequently the corresponding leave to remain stamp is no longer valid. The employer in question may or may not have notified the Home Office of the person not returning to work. If they notified the HO they would have written to your friend asking him to leave the UK or change status within 28 days of the receipt of the letter. Since neither happened your friend is an overstayer liable to removal from the UK - he/she better not get stopped by the police for routine enquiries such as jumping a red light. If the employer never wrote to the HO then he will get caught out at HSMP application stage because the immigration history of 'in country' applicants is carefully scrutinised.
2. WP's are employer and job specific i.e. they are
not transferable - your friend is working without authorisation and is therefore in breach of immigration laws yet again. Likewise his employer is also in breach of sec 8 of the 1996 Asylum & Immigration Act by employing someone who has no work authorisation.
3. The HSMP Team and Work Permits UK for that matter do not as a matter of practice consider any work experience gained whilst illegaly in the UK.
4. Salary slips are not the only acceptable form of income but they are the preferred document. You may also submit a P60 - record of earnings, income tax and national insurance contributions with employers letter detailing salary and bank statements showing credits from the employer.
Its not looking good is it

.