If a catcher decides not to attempt to throw out a runner, then it is called Defensive Indifference…and the runner is not awarded a stolen base! This makes no sense! That would be like if a shortstop goes deep in the hole and decides not to throw it to first, then the batter would not be awarded a hit because of defensive indifference!
If a player steals a base, and it goes uncontested, then the baserunner earned a stolen base!