I am with RJM. FWIW, most players after a certain round could at one time get good bonus money, but that is not done anymore. I actually know of a guy who got drafted very late and got good money and is still to this day a ML pitcher.
Now with the new collective bargainning agreement and draft spending things have changed bigtime. Also they cut down on the rounds, teams used to bail out after round 40.
Some teams do not need as many drafted players as others because they have less team rosters to fill. Those that don't want to sign the later players will offer a 1000 dollars perhaps hoping they will not sign. Would you have your son sign for that if he had a good chance to go back to finish his degree and help his team win a championship? Or HS player give up college for a 1000 dollars and a plane flight? I wouldn't. Teams can always fill in with free agents that will be released when the new guys sign or mature college seniors not drafted. A guy with pro experience is worth more to a team than someone who is a late pick and never played pro ball.
The truth is as a very late sign with no money, you will be sitting more than playing, or you will find yourself in what is called the complex leagues, played in the backfields of the spring training complexes along with the teams young latin players.