How to cancel the context of custom middleware plugin?

I want to cancel the go-routines invoked by my custom middleware as follows. However, these go-routines are continued to run even after the middleware is no longer in use. Is there any way to cancel the go-routine?

// New created a new Demo plugin.
func New(ctx context.Context, next http.Handler, conf *Config, name string) (http.Handler, error) {
	go func() {
		for {
			select {
			case <-ctx.Done():
				// ctx should be canceled when the middleware is no longer in use
				// in my expectation. However, it is not cancelled.
	return &Demo{
		next: next,
	}, nil