Individuals experiencing unexpected distressing events, shocks, often rely on their social network for support. While prior work has shown how social networks respond to shocks, these studies usually treat all ties equally, despite differences in the support provided by different social relationships. Here, we conduct a computational analysis on Twitter that examines how responses to online shocks differ by the relationship type of a user dyad. We introduce a new dataset of over 13K instances of individuals' self-reporting shock events on Twitter and construct networks of relationship-labeled dyadic interactions around these events. By examining behaviors across 110K replies to shocked users in a pseudo-causal analysis, we demonstrate relationship-specific patterns in response levels and topic shifts. We also show that while well-established social dimensions of closeness such as tie strength and structural embeddedness contribute to shock responsiveness, the degree of impact is highly dependent on relationship and shock types. Our findings indicate that social relationships contain highly distinctive characteristics in network interactions and that relationship-specific behaviors in online shock responses are unique from those of offline settings.