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I thought bond and treasury yields were supposed to be stable till maturity date.

Yet we often see reports like this:

Market upheaval intensified Friday as stocks and oil prices tumbled, while investors seeking shelter in haven assets pushed the yield on long-term U.S. government bonds to unprecedented levels. The yield on the benchmark 10-year Treasury note fell below 0.7% for the first time.

From WSJ's "Bonds Extend Rally as U.S. Stocks Decline" on March 6, 2020

Why do bond and treasury yields drop as more people invest in them?

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    The rate is stable if you hold the bond. If the bond price drops, a new buyer would pay less for it and receive the same coupon as you. Since he paid less for the bond, his yield is higher than you are getting. Conversely, if he pays more for the bond, his yield is less.
    – Bob Baerker
    Mar 6, 2020 at 17:54

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You are observing the difference between spot and par yield.

Let's assume you have a bond that costs 100 EUR and pays 1 EUR every year and then 100 EUR after 10 years. Its yield (both spot and par) is 1%. Because its par value 100 EUR is the same as its market price, the spot and par yields are the same.

Let's now assume that its market price rises to 110 EUR due to the increased investment into bonds by investors. That's the law of supply and demand. When demand increases, the price increases.

Now it still yields 1% of its par value, or in other words 1 EUR, every year, but still 100 EUR at the end and not the full price 110 EUR.

After this price rise, you will get 110 EUR back (ten times 1 EUR and at the end 100 EUR) for your 110 EUR investment. In other words, spot yield is 0%.

However, par yield is still 1% because the par value of the bond is 100 EUR.

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