[Shuriken] Direct particles to a point

It's possible (but laborious) to take direct control of the ParticleSystem's particles:

 public class ImplodingEmitter : MonoBehaviour {
     void Start() {
         StartCoroutine(Implode());
     }
     
     IEnumerator Implode() {
         if (!particleSystem.isPlaying) {
             particleSystem.Play();
         }
         
         //let the system do it's thing for a bit
         yield return new WaitForSeconds(3f);
         
         //stop emission
         particleSystem.emissionRate = 0f;
         
         //allocate reference array
         ParticleSystem.Particle[] particles = new ParticleSystem.Particle[particleSystem.particleCount];
         
         
         //this loop executes over several frames
         // - get particle list
         // - update each particle's position
         // - set particle list
         // - wait one frame
         for (float t = 0f; t < 1f; t += 0.1f) {
             int count = particleSystem.GetParticles(particles);
             for (int i=0; i<count; i++) {
                 particles[i].position = Vector3.Lerp(particles[i].position, transform.position, t);
             }
             particleSystem.SetParticles(particles, count);
             
             yield return null;
         }
         
         //once loop is finished, clear particles
         particleSystem.Clear();
     }
 }

Other option, and honestly it might be easier, is to just create your own GameObjects and move those. Each GameObject could have an emitter attached (say, a single particle set to simulation space "local"), or could just be a quad that happens to look an awful lot like a particle.