縫い掛けのワンピースを机の上に置いて買い物に行く
To put the unfinished sewn dress on the desk and go shopping.
Not sure I understand where the implication of the dress being unfinished is. I’m assuming it’s in 縫い掛け.
Would that mean if I said…
飲み掛けのコーラを… etc. it would be saying to leave an unfinished drink on the desk?
I’m pretty sure that’s correct. However, I’m not sure what rules govern when -かける can replace -かけ
Here’s 2 entries copied from Bunkei Jiten:
【かけ】
［R-かけ］
（1）やりかけの仕事が残っていたので、会社に戻った。
I returned to the office because I had some unfinished work.
（2）彼女の部屋には編みかけのセーターが置いてあった。
In her room was a sweater she was knitting.
（3）その本はまだ読みかけだったが、友達がどうしても貸してほしいと言うので貸したら、そのまま戻ってこなかった。
I was still reading that book, but I lent it to a friend who said he just had to have it and I never got it back.
（4）私は友達にもらった壊れかけのテレビを、もう5年も使っている。
For five years now I’ve been using a half-broken TV I got from a friend.
（5）食事を作ろうと思ったら、冷蔵庫の中には腐りかけの野菜しかなかった。
I was going to cook something, but all there was in the refrigerator were some vegetables starting to spoil.
Attaches to a verb stem and indicates that an action is in progress. Means either that someone has initiated an action that is still in progress, as seen in examples (1), (2), and (3), or that an event has started and is still in progress, as in (4) and (5).
【かける】
Whenever drunks on the train try to talk to me, I act like I don’t understand any Japanese.
（2）みんなに呼びかけて、いらなくなった衣類や食器などを持ってきてもらおう。
Let’s put a call out to people to have them bring clothes and dishes and other things they don’t need anymore.
（3）その子は、人と目が合うたびにやさしく笑いかけるような、そんな、人を疑うということを知らないような子だったと言う。
They say that she would give a kind smile to people whenever their eyes met, and was the sort of child who wouldn’t know what it meant to doubt others.
（4）リサイクル運動の市民グループを作りたいと思って、周りの友達に相談を持ちかけてみたが、みんな忙しいと言って話に乗ってこなかった。
I wanted to make a citizen’s recycling group so I brought up the topic with my close friends, but everyone said they were too busy and didn’t go along with my idea.
Attaches to a verb stem and expresses the effect an action has on others. 人に相談を持ちかける in (4) is an idiomatic expression, as are 問いかける (to ask someone), 語りかける(to talk to someone), and 誘いかける (to invite someone to do something).
2. R-かける〈partway〉
（1）友達に大事な相談の手紙を書きかけたとき、玄関のベルが鳴った。
Just as I was about to write an important letter to a friend, the doorbell rang.
（2）「じゃあ」と言って受話器を置きかけて、しまったと思った。彼に用件を言い忘れていたことに気づいたのだ。
I said “Bye” and was about to put the receiver down when I realized my blunder—I had forgotten to tell him what I’d wanted to say.
（3）その猫は飢えでほとんど死にかけていたが、世話をしたら奇跡的に命を取り戻した。
The cat was almost dead from starvation but, with my care, it miraculously revived.
（4）忙しい日々の中で忘れかけていた星空の美しさを、この島は思い出させてくれた。
This island has reminded me of the beauty of a starry sky, something which I had almost forgotten about in my busy daily life.
Attaches to a verb stem and means that an action has been initiated or an event is in progress but still has to be completed. Expresses either that an intentional action has been initiated but is still in progress, as in (1) and (2), or that an unintentional event has started and is in progress, as in (3) and (4).
Hi!
You are right, it’s in the cake 
. Here you can find the grammar point on 掛け.
Here are my notes on this grammar point as well:
かけ comes from the verb 掛ける ‘to suspend’, and may be attached to the conjunctive form or other verbs, in order to convey that they are ‘unfinished’. It behaves like a noun, so may be followed by the case marking particle の when attached directly to another noun, or by だ when at the end of a sentence.
かけ expresses that something is stuck somewhere in the process of happening. With verbs that express a momentary action (something that cannot be ‘half’ done), かけ will convey that the action was ‘on the verge of’ happening. However, with verbs that are ongoing actions, かけ will simply imply that they are ‘in the process’ of being done.
HTH!
I don’t think so, 飲み掛け would mean “in the process of drinking” but it does not imply a finished drink.
The sentiment of “unfinished” comes from the 終わり. If you keep in mind 掛け being “in the process of” and you attach the meaning of 終わり:
But for 飲む掛け
So an unfinished cola would actually be:
I think that might be taking things a bit too literal given that the implication of a “mid drink” would be that the action is yet to be completed. Going off of that implication, 飲み掛け works as intended.
There are other ways to use the -掛け stem instead of just “in the process of (doing)”
So 飲み掛け could also mean “half drunk” or “midway through drinking,” which both carry the implication of the action of “drink” being unfinished.
I wouldn’t think so… Would you be able to quote a native example?
As far as I can tell, 終わり掛け is not used that much, and when it is, it’s not about food, it’s about events that take time, e.g. 昼休み, 夏, 確認 (終わり掛ける – Vocabulary details – jpdb)
Maybe a different way to say it, is you cannot 終わる a drink, only a process. E.g. you can 食事を終わる.
Yeah good callout, I’m probably being too literal here. I had in mind the following:
VS
They both imply an unfinished drink being on the table, but in different nuances. And i thought the latter nuance might be better brought across by 終わる. But to @casual ’s point, if 終わる is not often used with food, then it’s likely this distinction is handled by other conjugations/grammar.
I’ll ask a Japanese friend if i get a chance and update
Edit:
also just realized the original Kanji is not 終わる it’s 縫い which is “embroidery” so it’s this “dress that has yet to be fully embroidered” aka “unfinished” dress. So OP’s question was already answered by the -掛け, i just went and gummed up the works with a completely different thought-path 
. Apologies friends!
The -掛け suffix applies to verbs.
縫い here is just the stem of 縫う meaning “to sew” or “to stitch”
縫い掛け would then mean “half-sewn” or “half-stitched”
And no worries, happens to the best of us!