We dream during the REM phase of sleep, which is the deepest, restorative phase. A normal sleep cycle lasts about 90 minutes, and during that time a normal person moves through sleep stages 1-4, then REM for several minutes, then back out through 4-1 before being only lightly asleep for a few minutes then entering another sleep cycle. Anything that suddenly and partially or fully wakes us out of REM sleep will cause us to become aware of our dreams. Medical conditions or symptoms can often do this.
I don't think this necessarily applies to most T1s, but in T2 diabetes if the person is overweight, they can develop obstructive sleep apnoea (OSA) syndrome, which interrupts sleep. These interruptions can happen anything from once an hour to once every minute. Often the person can never progress to REM sleep, but if they do, they are woken out of it and often report awareness of dreams and nightmares. OSA can also be caused by nose or throat anatomy disorders in people of normal weight. There is also a rarer condition, central sleep apnoea that can strike anyone, where the brain doesn't process messages to keep breathing during sleep as it should. Fortunately in OSA and CSA the body forces the person to wake up and breathe, so while it can cause health problems such as stroke, it isn't usually fatal in and of itself.
I've rambled on about my favourite subject a bit, sorry... the relevant point is that medical conditions can affect our awareness of dreaming.