but doesn't the NYPD have the most resources?
To monitor the internet and every job application website WITHOUT A WARRANT OR PERMISSION??? Really? There would be no realistic reason to do this, the cost would be high, and the beancounters at the NYPD would go nuts!
When you say resources, do you mean time and money, or do you mean the technical capacity?
All of the above.
They may not have the authority to monitor say McDonald's job application, but can't they monitor the sites a suspect visits and find out that she applied for a job @ Starbucks.com and then tell Starbucks not to hire?
No, they don't. And, assuming they did, why would they? That's a lot of time and effort to get back at someone. The smart move would be to let them start work and then arrest them at the job site! Why discourage the employer from hiring them if it might get the fugitive to come into the open.
But, you are free to remain as paranoid as you wish.
Bottom line: Deal with the problem. The warrant will NOT go away, and you (or whomever) will be looking over their shoulder for the rest of their life waiting for the day the cuffs will be slapped on until it's resolved.