An emergency set in the car
Short answer: Put a set of underwear, a pair of socks, a t-shirt and a towel in a bag in the boot. It takes little space and solves a surprise.
When it gets used
An unplanned overnight stay, an unexpected dip in the water, rain on the way home or a day that turns into an evening. All four happen, and a set in the car turns them into minor matters.
What goes in
A set of underwear, a pair of socks, a t-shirt and a thin towel. Bamboo fabric takes little space and tolerates sitting for a long time without getting worse. See bamboo underwear for men.
Keep it dry
Put the bag somewhere no moisture reaches and change the contents once a year. A bag that has sat two years in a damp car will smell. See bamboo towels and bamboo t-shirts for men.
Frequently asked questions
How much space does it take
A set plus a thin towel is roughly the size of a pair of shoes.
Should a blanket be included
In winter that makes sense. That is a different kind of emergency kit.
How often should it be changed
Once a year, or straight after it has been used.