I myself am not a landlord yet. But I plan to purchase a buy to let property. Anyway, topic isn't about my intentions.
My friend told me of a married couple wanted to take appartment he was letting. And when it came to agreement talk, spouse of a potential tenant said she wouldn't like to have agreement or anything, because she is not working. She didn't want totake any responsibility, etc. She relied om her husband.
A friend of mine refused them, justifying his actions by impossibility to have a deal without an agreement.
How often people intend to do something like this?

Hi.
Pretty often potential tenants tend to escape the tenancy agreement. And just a few landlords let them get away with it.
Actually, all adults living in a rented property have to be named on the tenancy agreement, in addition to signing it.
So, inform your friend to never let property without signing the agreement, ok?

Normally, all adults living in a rented property have to be named on the tenancy agreement, as well as they should sign it.
This refers to regular tenancies and short term lets.
So, your friend should not worry on this subject. He acted like he was supposed to. If there is no agreement, there is no renting out.

I kind of disagree with this one. I would have made a note that she resides there, but would not let her sign the agreement. She would not be able to pay rent as she has no income and if the worst happens and he leaves, she'll have no right to stay at the property too. In my experience, landlords often dont like including onto tenancy agreement a partner/co-habiter, etc who is not working. As far as tenancy agreement is concerned, my view is that it's beneficial to tenants as well as landlords as apart from responsibilities it gives certain rights too.

+1
that's what it says online...

therefore, you friend could've signed an agreement with that lady's husband and mention her name in the agreement.