Eccentric loads are generally what will create the added stresses on soft tissue and joints. By eliminating those eccentric loads, it will help eliminate extra damage to the soft tissue and can help progress specific issues at specific points during a rehabilitation.
It really all depends on the type of injury as well and what point of healing the injury is going through. Eccentric work is critical to proper rehabiltiation, but is best to be done in a controlled situation at the proper time during rehab.
For exmaple, if the injury is an acute and significant hamstring strain, then I would avoid too much activity with it all together until it is ready to handle extra loads, then you could progress to an overall concentric based strengthening program (sled work) and use a rehab focused and controlled eccentric work. From there, progress to your standard strenghtening work with eccentric components involved. If the injury was anterior knee pain, it would be beneficial to do sled work to avoid the eccentric loads on the patellar tendon and excessive anterior shearing forces on the knee. Controlled eccentric work would help develop and strengthen the patellar tendon to reduce the chance of future issues.
These are just my opinion on it from my experiences, but have found them very useful, especially with ACL repairs, mensical issues, and patellar tendinopathy/anterior knee pain.