Final Fantasy VII
SOLDIER are ShinRa's Elite Fighting Force and they're brought in when a situation requires more muscle than the normal ShinRa army can deal with. This is because they have superhuman attributes, including enhanced strength and agility.
They were first introduced in Final Fantasy VII by Cloud Strife, who claims to be a member. Some other lower ranking members are also encountered in the ShinRa Headquarters when it is infiltrated.
The Demise of SOLDIER
Although Cloud believed he was a member of SOLDIER, these were false memories and despite having the physical attributes to back up his claims, he was never an official member.
With no recognisable 1st Class SOLDIER still in existance, when the ShinRa company starts to fade away so do memories of SOLDIER.
Before Crisis: Final Fantasy VII
During Before Crisis, SOLDIER makes a few brief appearances. One major aspect of their involvement in the game actually ties in with the Turks.
During the game, the Turks are charged with recruiting new candidates for SOLDIER admission, with one of these candidates being Azul the Cerulean. Sephiroth also makes an appearance, as he is President Shinra's trump card in the war against AVALANCHE.
Other SOLDIERs that appear during Before Crisis are Zack Fair and Essai and Sebastian.
Dirge of Cerberus: Final Fantasy VII
Deepground is a hidden section of SOLDIER which houses its potentially more deadly soldiers. They pay little part in the proceedings of the Final Fantasy VII mythos until Professor Hojo manages to take over the body of Weiss the Immaculate.
Upon the defeat of the Tsviets, there are no remnants of SOLDIER left, aside from the memories inside Cloud's head.
Crisis Core: Final Fantasy VII
Crisis Core signals where the decline of SOLDIER initially happens, as Genesis Rhapsodos leaves and Angeal Hewley follows. Although Zack Fair is promoted to a SOLDIER 1st Class, this does little to stop the mass exodus.
When both Sephiroth and Lazard Deusericus leave, it all but signals the end for SOLDIER and although it does continue in some form, it doesn't hold anywhere near the same amount of respect without its elite 1st Class ranks.