Can I lose money in a money market fund or a 'safe' bond fund?

It's uncommon but not impossible, and understanding why helps you set realistic expectations. Money market funds aim to hold a steady $1 share price and rarely lose value, but they're investments, not FDIC-insured deposits, so a stable price isn't guaranteed in extreme conditions. Bond funds are safer than stocks but not risk-free: when interest rates rise, the prices of existing bonds fall, so even a high-quality bond fund can post a negative year, as many did during sharp rate increases. The longer the bonds the fund holds, the more its price swings with rates. For money you truly cannot afford to see dip at all – an emergency fund or a near-term down payment – FDIC-insured savings, CDs, or short-term Treasuries are the more literal definition of safe. 'Conservative' still means some movement, just a lot less than stocks.