Strength training is established as a valid and effective therapy in stroke. Weakness is a key impairment that develops after hemispheric stroke. Furthermore in chronic stroke residual weakness is complicated by accelerated ageing of the neuro-musculoskeletal system so that patients tend to become weaker over time.
Strength training is also an important component of falls prevention. key muscles in the legs are important for maintaining good balance.
There is little evidence that Strength training causes harm. Such training does not increase spasticity.There may be the usual precautions with any programme using progressive resistance training where there is an increased risk of injury to muscle or over-training if carried out over zealously. Gradual increase in intensity. well controlled exercises and having sufficient recovery periods between strengthening training periods will reduce these risks.
When thinking of strengthening it is important to consider building up muscle endurance and also speed of contraction (Power) and not just pure strengthening. And there may be special value in training muscles for activities that the person wants to improve in (task specificity) rather than doing strengthening exercises in isolation
For a review of strengthening programmes for stroke see:
Ada, L., Dorsch, S., & Canning, C. G. (2006). Strengthening interventions increase strength and improve activity after stroke: a systematic review. Aust J Physiother, 52(4), 241-248.