Hmm... Â Interesting never heard that one before, here's something
To understand where do thoughts go, we must first decipher how are memories formed?
Things we do or think can be classified into short and long term memories. Short term working memories are processed in our pre-frontal cortex whereas the long term memories are processed and then stored in much deeper part of our brain known as hippocampus.
Fun Fact: We can keep up to 150 thoughts in our short term memory, after that it overflows and if I don't take a nap or clear my mind, I become absent minded **
  A short-term memory's conversion to long-term memory requires the passage of time, which allows it to become resistant to interference from competing stimuli or disrupting factors such as injury or disease. This time-dependent process of stabilization, whereby our experiences achieve a permanent record in our memory, is referred to as "consolidation."
  Memory consolidation can occur at many organizational levels in the brain. Cellular and molecular changes typically take place within the first minutes or hours of learning and result in structural and functional changes to neurons (nerve cells) or sets of neurons. Systems-level consolidation, involving the reorganization of brain networks that handle the processing of individual memories, may then happen, but on a much slower time frame that can take several days or years.
  Consolidating such synaptic changes requires the synthesis of new RNA and proteins in the hippocampus, which transform temporary alterations in synaptic transmission into persistent modifications of synaptic architecture. ***
Hippocampus stores our memories or thoughts as different files (files beng emotions, smell, visual stimuli) in different folders (folders being various neural connections and different parts of the brain, as if I have divided my hard drive into parts - one part I use to store movies, one for academia related stuff, one for music).
Hippocampus only stores fact based memories i.e when you make an effort to safekeep a memory or thought. If you had a thought and just let it pass by it is more likely to be forgotten by your conscious and unconscious mind too, but if you make an effort i.e. writing down the thought or brainstorming it with someone; you are more likely to recall it at some point.
Being said that, memories are not saved as a whole in hippocampus. They are saved in parts, when recalled brain brings together these parts like the pieces of jigsaw to complete a picture.
Now the problem is, there are many similar pieces of puzzles in your mind/brain, sometimes our brain brings in a different piece of various puzzles which fits perfectly but is not actually a part of the same puzzle - when such things happen a memory is tainted or mutated - this blind spot is used by hypnotist, street artists, psychology practitioners, dharm gurus and manipulators to induce a new thought/memory in someone's brain.
One can also forget these memories due to illness where hippocampus is compromised and not able to form any neural connections read Alzheimer, dementia, any physical damage to the brain.
And that is how you lose your thought or memory. It doesn't go away just get mixed up. It is all about recalling the right instance.
