Fillet error ?
@dmfrazier wrote:
.....
The FILLET command is not intended to be used to "fillet" a line and an arc, which is illogical, thus the unexpected and undesirable result.
Don't listen to them -- it's not at all illogical. The Help entry for FILLET even demonstrates Filleting a Line with an Arc. If you look at those illustrations, you'll see that the result can come out differently depending on exactly where you pick on the Line and the Arc, in a potentially different relationship than when Filleting two Lines, so that may be the source of the problem in some situations. But I can't explain the one where the resulting Arc is the rest of the circle that the desired result would be the other portion of.
If Polylines are involved, there was a time when you couldn't Fillet a Polyline arc segment to anything, but newer versions allow that in some relationships -- an arc segment to another segment in the same Polyline, whether arc or line, and an arc segment to a separate Line, but apparently not either an arc or line segment to a separate Arc. But in those situations, it simply doesn't allow it -- it doesn't give that kind of oddball result, so something else must be going on.
For one possibility when a Polyline is involved, see >this< for a suggestion that may help, at least sometimes.
Kent Cooper, AIA 
@dmfrazier wrote:
In the context of the OP's provided images and given the "basic" definition of "fillet" ("a concave junction formed where two surfaces meet - as at an angle", or "a concave strip of material roughly triangular in cross section that rounds off an interior angle between two surfaces"), I think it's fair to characterize filleting a line with an arc as "illogical", particularly when the arc already represents a "fillet".
I wholeheartedly disagree. The "basic" definition doesn't in any way limit the "surfaces" to being straight/flat, and it's common to [for example] fillet-weld a curved surface to a flat one, or to another curved one.
The Arcs in their images that they want to connect to Lines with smaller-radius rounded corners clearly do not represent anything like a fillet, any more than the tubular column in this first image does.
But in the end, the fact remains that AutoCAD can do this, and what's needed is not to tell the OP they're doing something they shouldn't [they're not, and they're successfully doing it in many places], but to figure out what is causing it to not work in some situations, whether that's the steps they're taking, or out-of-plane geometry, or whatever else it may be.
Kent Cooper, AIA
@Anonymous wrote:
It here. DWG please see file attached.
One potential problem is that your "closed" Polylines are not closed, but merely end at the same place they start [5 vertices for a 4-sided shape], which certainly can cause problems in some operations. I tried Trimming out from the Lines/Arcs originals, and connecting into Polylines using PEDIT/Join, and I got the same result. I tried again using JOIN, and they at least came out actually closed, but the same weird things happened at corners. When I built my own closed 4-sided Polyline with two opposite line segments and two opposite arc segments, Filleting worked fine. Your original parts all seem to be in the same plane, which is one thing I wondered about [but maybe not if you go way down in decimal places? -- I didn't check that]. I don't have anything else to suggest for now....
Kent Cooper, AIA