Runaway works as a noun (meaning someone or something that has run away) and an adjective (meaning out-of-control, unrestrained, or escaped), but it does not function as a verb. If you need a verb meaning to flee or to escape, use the two-word phrasal verb run away.
Run away is just one of many phrasal verbs with corresponding one-word nouns/adjectives. Check up, work out, and blow up are a few other examples. The one word forms almost never become verbs in standard usage.
Runaway (noun, adjective)
Crystal Harris, Hugh Hefner’s 25-year-old runaway bride, is putting her 3.39-carat engagement ring up for auction next month. [Los Angeles Times]
Yet, the runaway train ploughs on, scarcely aware that it ran over the people who make the brakes. [Irish Times]
Seven of the 11 children were listed only as missing and six were presumed to be runaways from broken homes. [The Province]
Run away (verb)
A missing Porirua teen is feared to have run away to Los Angeles to meet a person she met on Facebook. [Stuff.co.nz]
Pat Juras didn’t run away and hide during the opening mile. [Buffalo Grove Countryside]
These are the children who are most likely to run away from home. [Guardian]