Thanks a lot Grmf! , for such a quick fix, giving me peace of mind.
BTW, when do you sleep? 

Don't ask him to sleep: we need him here at anytime 

Am I obliged to sign the '"Avenant au bail"'?

No. As you would loose the best payer, I would advise to refuse to sign.

Yes. Nobody can force you to sign this avenant, downgrading the payment safety.

Yes. This is what I would recommend.

I signed a one year rental contract,  to rent my apartment in Brussels capital Region, with a single lady(divorced/separated) with a child, in 2012; Then we renewed it three times, we made it into a 9 nine year contract for the third renewal. Initial contract and subsequent two rentals contract renewals were signed solely by the lady. The final renewal which became a 9 year contact was signed by the lady plus a man who moved and lived with her.

Here is a break-up/dates for each contract/renewals:

1. initial contract  (lady only) for one year [1/10/2012~30/9/2013]

2. first renewal  (lady only) for nine months [1/10/2013~30/6/2014]

3. second renewal (lady only)  for one year [1/7/2014~30/6/2015]

4. third renewal (lady + man) for nine years, from the initial contract date [1/7/2015~30/6/2021?]

5. The initial contract and renewal until 2014 were from PIM templates from year 2009, a version from December 2009.

6. The last contract template is bail de résidence principale pour un immeuble sis dans la Région de Bruxelles-Capitale (2014v4)

The lady doesn't have constant income, no stable job and have bad payment history.
She delayed rental payment for a few times since 2012. Couple of times she paid her rental arrears within couple months.
Now, even with co-locaitaire,  it took both of them 13 months delay to pay a pending rent from 2015.

I only renewed the contract for the third time, ending up the 9 year contract, as the man who moved/lived with her together,  had a stable job and their cohabitation seemed stable. Now, that man who has been living with her, cwants to leave her and requests me to sign  '"Avenant au bail"', quotes me the link Le départ anticipé d'un colocataire en cours de location".

If I sign '"Avenant au bail"',, I am worried for the future rents plus it may be very difficult for me to evict the lady,  since she is living alone, with a 10 year old child.
The best option for me would be, if both leave the apartment together, to avoid hassles for next ~5 years. I am looking for a safe way to get out of 9 year deadlock.
Although, I would be happy to honour the 9 year lease if both are staying together.

1. Am I obliged to sign the '"Avenant au bail"'?

2. Do I have the right to refuse to sign '"Avenant au bail"'?

3. As I am unwilling sign '"Avenant au bail", Could I recommend both of them to give 3 months notice and leave together, at their convenience? 

Thanks in advance for guiding to walk out of this mess.