На тарелке осталась одна тефтеля.

Because на тарелке means on the plate as a location, and Russian uses на + prepositional case for static location.

• тарелка = nominative singular, the dictionary form
• на тарелке = on the plate, location
• на тарелку = onto the plate, motion toward it

So:

• На тарелке лежит вилка. = A fork is on the plate.
• Положи вилку на тарелку. = Put the fork onto the plate.

Here nothing is moving onto the plate; it is simply remaining there, so на тарелке is correct.

In the past tense, Russian verbs agree with the subject in gender and number.

The subject here is одна тефтеля, which is:

• singular
• feminine

So the verb must also be feminine singular:

• остался = masculine singular
• осталась = feminine singular
• осталось = neuter singular
• остались = plural

Since тефтеля is feminine, you get осталась.

Because один (one) behaves like an adjective and must agree with the noun in gender, number, and case.

Since тефтеля is feminine singular nominative, the form is одна:

• один стол = one table
• одна книга = one book
• одно окно = one window

So:

• одна тефтеля = one meatball

It is in the nominative singular.

That is because it is the subject of the sentence: it is the thing that remained.

Even though it comes after the verb, it is still the subject. Russian word order is much freer than English word order, so the subject does not always have to come first.

You know it from the grammar, not just the position.

There are two main clues:

1. The verb agrees with it
   осталась is feminine singular, matching тефтеля.

2. The form makes sense as nominative
   тефтеля is the thing that remained, so it is the subject.

Meanwhile, на тарелке is just a location phrase: on the plate.

Russian often puts the setting first and the important item later:

• На тарелке осталась одна тефтеля.

This is very natural and often sounds like: On the plate, there was one meatball left.

Осталась comes from остаться, which means to remain, to be left, to stay behind.

So this sentence does not just describe where the meatball is. It suggests a result: after something happened, one meatball was left.

That is different from:

• лежала = was lying
• была = was
• находилась = was located

Compare:

• На тарелке лежала одна тефтеля.
  = One meatball was lying on the plate.
  (just description)

• На тарелке осталась одна тефтеля.
  = One meatball was left on the plate.
  (something used to be different; now only one remains)

Осталась is perfective because it presents the situation as a result: in the end, one meatball remained.

This is exactly the kind of thing perfective verbs often do in Russian: they show a completed outcome.

• осталась = ended up remaining / was left
• оставалась = was remaining / kept remaining

In this sentence, the speaker is not focusing on a process or duration. They are focusing on the final state.

You could use the imperfective in a different context, for example:

• На тарелке долго оставалась одна тефтеля.
  = One meatball remained on the plate for a long time.

There the ongoing duration matters, so imperfective makes sense.

In this sentence, одна clearly means one.

That is because it comes directly before a singular noun and agrees with it:

• одна тефтеля = one meatball

Russian один / одна / одно / одни can sometimes mean alone, but then the structure is different.

Compare:

• На тарелке осталась одна тефтеля.
  = One meatball was left on the plate.

• Тефтеля осталась одна.
  = The meatball was left alone / was by itself.

So the same form can have different meanings, but the sentence structure tells you which one is intended.

Yes. Russian word order is flexible, and different orders change the focus or emphasis.

The given order:

• На тарелке осталась одна тефтеля.

puts the location first. It feels like the speaker is setting the scene and then telling you what was there.

You could also say:

• Одна тефтеля осталась на тарелке.

This puts more focus on one meatball.

Both are grammatical. The difference is mainly about emphasis and information flow, not basic meaning.

Because Russian does not need a dummy subject like English there.

English often says:

• There was one meatball left on the plate.

Russian usually just gives the location and the thing/event:

• На тарелке осталась одна тефтеля.

So Russian expresses the same idea without an extra word meaning English there.

This is very common in Russian. English existential sentences often become simple Russian sentences with:

• a location phrase
• a verb
• the noun

Yes, тефтеля is a singular form, and the plural is usually тефтели.

However, many learners notice the plural more often than the singular, because people often talk about meatballs as a dish in the plural. In everyday speech, you may also hear other forms such as тефтелька.

So this sentence is grammatically fine, but it is normal if the singular looks less familiar to you than the plural.