A large number of M14s remained in arsenals and have been available for issue. Remember that the M14 was only the standard issue rifle from 1959-1970, and was only produced from 1959-1964. Nevertheless, about 1.5 million were manufactured. It should be considered, too, that most M14s never saw combat. As a result, many of those in the inventory were new or virtually new.
The new lease on life for the M14 came with the deployment of US troops to Afghanistan and Iraq. In Afghanistan especially, the M4 carbine did not have the range to engage the Taliban or other insurgents armed with AK47s. As a result, Designated Marksman Rifles (DMR) based on the M14 has seen substantial usage. Actually, the USMC was using a DMR version of the M14 modified at the Precision Weapons Shop at Quantico during the 1990s. These rifles were intended for FAST (Fleet Anti-Terrorism Security Teams), observers on Scout/Sniper teams, and some other special troops
Another user of rifles based on the M14 has been the US Navy SEALs. The MK 14, Mod 0 EBR (Enhanced Battle Rifle) has been widely used by the SEALs. Special Forces spotters on sniper teams have been armed with the M25, a precision version of the M14. Some Combat Applications Group (AKA Delta Force) and DevGru (AKA SEAL Team Six) helicopter snipers have used sniping rifles based on the M14.
To answer your question, though, a large number of M14 based rifles being used as DMRs have been built from M14s in military armories. For some of the precision rifles, only the M14 receiver was used along with some internal parts, while other parts including barrels were obtained elsewhere.
I do not know of any US military contracts granted for complete rifles based on the M14. Springfield Armory not only offers the semi-auto M1A, which is based on the M14, but also semi-auto versions of the M21 and M25 sniping rifles. Since most M14 rifles were originally issued without the selector switch installed, they were used as semi-autos anyway. Since the semi-auto M1A barreled action will fit in many of the enhanced stocks developed for military use, it is possible to build a DMR that is very similar to those used by the armed forces.
CREDIT: Leroy Thompson