the new york state attorney genrals office is trying to serve me so that i can give a deposition about the use of spoof cards at a former employer. how long can or will they attempt to find me before they give up?
It depends in what context they are seeking your testimony. The court could hold you in contempt and compel your imprisonment if you refuse to testify (and hold you until you do). Without more details, it's unclear in what capacity they are seeking your testimony (as a witness, suspect etc.). Depending upon how important they consider your testimony, they may continue to pursue. The bottom line is that you don't want intentionally avoid legal process. It could have bad consequences. Criminal punishment? Unlikely, but the question requires more information.
