The design of these headphones includes a microphone on the outside and on the inside of each earcup. The outside microphone detects outside noise. The inside microphone monitors what you are hearing and when it detects that the outside noise is present inside, the active noise-canceling circuits remove that noise. This happens fast enough that you perceive a significant reduction in the outside noise getting to your ears.
The airspace inside the earcup is a tuned chamber defined by the shape of the foam in the ear cushion. This is important because with the inside microphone in close proximity, but at a 90-degree angle to the speaker, the circuit must be designed to eliminate the normal feedback that occurs.
If the foam in the ear cushion has weakened/deteriorated to the point that it no longer has it's original shape, (in particular the lower half of the ear cushion), the size and shape of the air chamber inside of the earcup is directing more of the speaker sound toward the microphone than the design can compensate for causing audio feedback to occur. You are hearing that feedback.
On my QC-3 headphones, I can cause the feedback squeal in both earcups, with the left earcup being more sensitive to the shape change than the right.
It is probably time to replace the ear cushions. If so, they are available from Bose for $35/pair.
QuietComfort 3 Acoustic Noise Cancelling Headphones Bose Product Support
They are also available aftermarket at Amazon.com for $16.99/pair
Replacement Earpad ear pad Cushions For Bose QuietComfort 3 QC3 Headphones...
Bluecell Pair of Replacement Earpad Ear Pad Cushion for Bose Quietcomfort...