, my mum and dad claimed ESA as my mum has been ill since

Hi,
my mum and dad claimed ESA as my mum has been ill since 2006 and my dad has had to care for her, my mum has arthritis, mental health issues and also heart condition which has not been diagnosed with any illness name.my mum has numerous medicines on repeat prescription. my mum has been on the sick for over 6 years. recently mum parents were called at the job centre and a work assesment was done on them. the
person doing the assessment said my mum is not fit too work but told my dad that he will need to sign and there esa will stop and they will now be on jsa. My dad told her he cant work as cares for my mother so she said that he needs to fill in PIP form once that passes then can fill a carers form and then he will not be called for work.
my dad is to sign on the 16/feb but I was wondering would he have grounds to get a sick note from his doctor as he cares for my mum and should not really be called in to sign as my mum always needs to be supervised due to her mental health. she doesn't remember anything, she can keep the cooker gas running or the water tap or just sit for hours in deep thought. we are scared that by leaving her unattended for him to sign might put her in harm
me and my brother and sister all work so cant step in for him to supervise our mum
can he get a sick note from the doctor for him