continue to live; endure or last; "We went without water and food for 3 days"; "These superstitions survive in the backwaters of America"; "The racecar driver lived through several very serious accidents"

continue in existence after (an adversity, etc.); "He survived the cancer against all odds"

support oneself; "he could barely exist on such a low wage"; "Can you live on $2000 a month in New York City?"; "Many people in the world have to subsist on $1 a day"

live longer than; "She outlived her husband by many years"

As it relates to separation agreements, when a separation agreement survives, it maintains a separate existence versus one which merges and becomes part of the divorce decree. Since women are usually the one who receives payments from the divorced spouse, it is usually best for them to have the document survive (rather than merge). p 33

to stay alive or in existence