I had a few comments to add along with the prior reply. A bond itself does not change its payout, as stated, unless it is a specific type that does so, like an iBond. Also, a bond fund holds mostly fixed securities.
However, a bond fund will post what is called an average duration, usually something like 7 years for a medium term fund. So generally, half the bonds will mature before that time and new bonds will be purchased, which will yield higher amounts due to the inflation.
So, over time, a bond fund's payments do increase with inflation, just not quite as fast as the inflation rate. If inflation stabilizes, the value of the fund shares will recover as well. Over time, expect bonds to yield slightly above inflation and there are many sites which show the value of holding bonds long term. Like stock funds, you should think of bond funds as long term investments you hold for 10 plus years.
Also, the expected rate of inflation is already priced into the bonds yields, so it is only 'higher than expected' inflation that decreases bond values, not raw nominal inflation.
Trying to time in and out of bonds by guessing future inflation rates better than the market is just as futile as trying to predict the economy to time stock purchases on dips (a generally accepted view for individual investors, though hedge funds and other quantitative analysts sometime try).
I would recommend an asset allocation plan based on a solid understanding of portfolio theory and your investment time horizon. If your hoizon is 30 plus years, 0 to 20% bonds is a reasonable allocation that generally does not hurt returns over a 30 year horizon and somewhat smooths the annual swings.