This looks like a typical halogen light bulb. They are:
- Extremely hot
- Very bright
- Very small
The combination means that, until bright, efficient and affordable white LEDs came along (LEDs have been around a long time, but only recently have white LEDs become bright enough and inexpensive enough to replace halogen and incandescent bulbs in regular usage), halogens were the way to get a lot of light out of a reasonably sized portable lamp.
However, the extremely hot + very small meant a requirement for a large open reflector to diffuse the light and to dissipate the heat. For lamps that shine up instead of down (which coincidentally takes away the "bulb fall on me" fear), they were normally uncovered, leading to many fires if someone (on purpose or by accident) let clothing, curtains or other flammable objects lie on top of the lamp. As a result, the last revision of halogen torchieres included a metal grid cover (and available as a safety add-on for many existing lamps, in lieu of the manufacturers being forced to recall them all) which would prevent at least some fires without actually trapping heat (which would cause a lot more fires).
The end result though is that this type of lamp simply can't be covered.
As far as the bulb falling out, that actually isn't a big concern. Halogen bulbs have, in my experience, pretty strong connections. In fact, if anything the opposite is true - they are hard to remove when they burn out and need to be replaced. So don't worry about that part of the problem.
I would consider replacing it when you can. Hard to say what you have, but if it is a 200W bulb then a replacement LED (not just a replacement bulb, you would really need to replace the lamp) might use 30W. If you use the lamp 6 hours a day, that saves 1 kWh per day. At a typical rate of \$0.15/kWh (many places are higher, many lower) that's 0.15/day = \$55/year - the energy savings add up pretty quickly.