Not clear how it is related to tax and what welfare and rent is connected.

Not addressing anything related to welfare, let’s approach the rent:

- Rental agreement can  be verbal, but it applies mostly to disagreement relate to tenant x landlord ( one can be labeled landlord if renting a room), for any other purpose hard to especulaste trying to antecipate each situation. 

- According to tax laws Any rental for more than 14 days a year must be reported as income

- when comes to verbal agreement proving that a contract existed does not require extraordinary efforts, in some cases a simple combination of , text messages, emails, photos, phone records, mail  etc may be accepted.

- there are tax benefits if you rented a room one month of the year.  In some cases taxes write offs may even reduce one’s adjusted gross income.

- not issuing a receipt does not necessary benefits the landlord, depending on the situation  it can actually count against the person.

- lying or defrauding Government agencies is never a good idea, usually criminal charges follow attempts to recover $$, one can always come clean retroactively instead of waiting or being blackmailed. Blackmailing is illegal, if a person requests something in exchange to not report another, it is blackmail, in situation like this people usually benefits from coming clean retroactively and reporting the blackmailer. 

Disclaimer: I am not a tax or lawyer, I am only expressing personal opinion which shall not be regarded as professional  advise. It is always recommend the person seeks professional advise.