Because this is not a common event, I do not think there is any single standard word that fits. However, during the American Civil War in 1864, individuals from one side could avoid the draft by paying what was called a commutation fee of $300 (about $10,000 today)
Enrollment Act and Commutation (Wikipedia)
Otherwise certain individuals can get an exemption to avoid conscription. Reasons for exemption can include age, enlistment in a different military service, certain vocations (such as clergy), or medical/health restrictions. Women are also typically exempted from conscription (although not in every country).
Certain individuals can also get a deferment to delay their military service to complete their education, because of medical restrictions or family obligations, because they work in certain important fields (such as scientists, farmers, key manufacturing workers, some government employees, etc.) and various others.