For Dracena's lopping off the top is a very good idea. Then you will get 2 or 3 new branches coming out, maybe even more, with nice fresh green leaves that are not all brown and scruffy. Just make sure after you do this, you put it in the brightest window you have where it gets lots of bright light, perhaps even some morning sun. Also pull off all that brown shabby stuff on the trunk. That will make it look much nicer. I have done this with three of my plants to get bushier plants. Here are pictures of my Dracena. It is a variegated Dracena. There are three plants in this pot. All three plants have been lopped so they start bushing out more, and growing new limbs.
In the picture above you can see where they cut the Dracena and lopped it off. See how three new branches grew out where they lopped it off.
In this picture, you can see where two of the Dracena's are lopped off.
Here is a picture of the three planted together in the pot. All three have been lopped off so more branches would come out.
This will not hurt your plant, just be sure and give it plenty of bright light and sunshine to encourage growth. I also rotate my plant so that all sides of the plant are getting the brightest light at the window. I turn this plant once per week, about a third of a turn.
