Is it carbs you're avoiding or fibre? They're not the same thing. Or are you avoiding both? And if you're avoiding carbohydrates, what's the reason for that?
EDIT: Ok I reread your post - I think you mean low fibre, as the title of your thread says, but this bit of your post:
You meant "can I eat on a low fibre diet" instead of "on a low carb diet"? Sorry, I'm probably just confusing you!
Some low-calorie, low-fibre, (and some low-carb) foods:
Pretty much any lean meat and fish
Eggs and low fat dairy products like yogurt, low-fat cheese spread, cottage cheese
Smooth soups
Bananas and avocados are low-fibre, I'm not sure if they're low-carb, that would depend on what you count as low. Also almost any tinned fruit and stewed apple should be fine. You might be alright with well cooked carrot and potatoes without skin.
These are not low-carb, but plain crackers, white rice, and white bread are low in fibre and have pretty much the same amount of calories as their whole-grain counterparts. The same with low-fibre breakfast cereals like cornflakes and rice krispies, they don't differ much in calories from high-fibre cereals, whole-grain cereals.
Or maybe you could find out about meal-replacement drinks aimed at dieters?