When stars like the sun die their core runs out of hydrogen fuel and it contracts under the weight of gravity, however

Question: When stars like the sun die their core runs out of hydrogen fuel and it contracts under the weight of gravity, however some hydrogen fusion will occur in the upper layers of the star. Have you ever discovered a start that has had hydrogen fusion occurring in its upper layers?
- Keywords:
  space,
  star,
  universe
Asked by qureshir to Nick on 10 Mar 2014.
- Nick Wright answered on 10 Mar 2014:
  
  Yes, they’re sometimes called red giants. Astronomers have learnt how to spot them from their colours, and if you ever visit an observatory maybe someone will show you one!

Question: When stars like the sun die their core runs out of hydrogen fuel and it contracts under the weight of gravity, however some hydrogen fusion will occur in the upper layers of the star. Have you ever discovered a start that has had hydrogen fusion occurring in its upper layers?