Most everyone has been through it.
You stand in line with other suitors and then systematically bypassed for one reason or another. Too slow, not smart enough, not pretty enough, are an Arizona Cardinals fan, etc.... It happens in life with friendships, careers, and marriage. It also happens in the NFL when looking for a job. After all, there were only 254 openings in which thousands have applied.
But some are granted a second chance. Players that are not selected in the initial 7 round draft can be supplemented on a team roster via the undrafted free agent tag. While most face an uphill battle in make the final squad, WR Laron Byrd and C Scott Wedige made the team last season.
And one of the best reports for the UDFAs is this site, which has some interesting names reportedly coming to Cards camp:
With four secondary players, two wide receivers and one offensive lineman supposedly (and their will be more and the list is probably not completely accurate - negotiations being what they will) joining the team for mini-camps and organized training activities another small group has made the big time and will avoid being the indignation as not being the last one picked.