yes,but they would have to have big mental issues.
It's called "separation anxiety", or simply a state of anxiety where you fear separation from someone you have an emotional attachment to. Symptoms include recurring distress, and persistent, excessive worrying about losing the person you have the attachment with.
some do
Arcana - 2012 Separation Anxiety - 1.4 was released on: USA: 18 June 2012
Forensic Files - 2000 Separation Anxiety was released on: USA: 8 January 2010
The child exhibited separation anxiety upon his mother's departure.
if one has been unusually close for extended periods of time to a certain person and then is separation, the sudden lack of closeness and communication and dependency can lead to anxiety and fear
Separation Anxiety Disorder
Arcana - 2012 Separation Anxiety 1-4 was released on: USA: 18 June 2012
Snoops - 1999 Separation Anxiety 1-6 was released on: USA: 31 October 1999
Spider-Man and Venom Separation Anxiety - 1995 VG was released on: USA: 1995
ER - 1994 Separation Anxiety 15-11 is rated/received certificates of: Netherlands:12
Spider-Man and Venom Separation Anxiety - 1995 VG is rated/received certificates of: USA:K-A