Dangers and threats, duty and responsibility, failures and mistakes, loss of control

Family members being at home during a break-in or burglary
A loved one taking on a dangerous job (rescuing someone who's fallen through the ice, fighting a fire, delivering medical supplies to a remote location, etc.)
The character's partner being targeted by a controlling, vengeful ex
Children being in a building where there's a fire, active shooter, or other threat
A loved one being used as a human shield
A family member being taken hostage
Being out with family and running into someone violent
Discovering there's a sex offender working at a child's school
Someone the character cares about agreeing to meet with criminals (to pay a ransom, pick up contraband for a delivery, pay a bribe, etc.) 
The character's family being targeted by criminals to dissuade them from testifying 
Being exposed to a virus at a work lab and unknowingly bringing it home
Family members living in an area where war has broken out
A tsunami, earthquake, or other natural disaster striking the place where the character's grown children live

Being unable to focus on anything but worry
Dropping everything to concentrate on the threat
Engaging the police (filing a report, being questioned, etc.)
Wanting more information but not getting it
Staying near a phone, computer, or location in hopes the loved one makes contact
Fielding phone calls from concerned family and friends 
Having to put on a brave face around family (especially if children are present)
Having to deal with reporters camped in front of the character's house
Not being able to get in touch with the endangered party
Disagreeing with a spouse or parent about how the situation should be handled
Having to pay a lawyer, bodyguards, or someone else