Is a person susceptible to singles/chicken pox if they've had shingles and someone in the house has chicken pox?

Yes & no: If you have ever had chicken pox the virus will be with you for a lifetime. It hibernates in nerve centers along the inside of the spine and can become active again by coming out along a nerve tract.Your prior chickenpox should make you immune to CP & shingles is not triggered by CP exposure.You can have shingles again if your resistance wains. A vaccine is avail to boost your resistance.

Shingles: Once you have had shingles, it means that you already had or were infected with chicken pox years before. Would be very rare to get chicken pox again. Shingles vaccine is always a good idea to reduce chance of repeat shingles in future or to at least reduce severity if it happened again.