The most common and most likely answer to this crossword clue is the 8 letter word RATIONAL
I've seen this crossword clue in The Daily Telegraph
R
A
T
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O
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L
More clues leading to the result RATIONAL
- Desert island left having good grounds
- Helping a learner is sensible
- Helping a learner to be sensible
- Like some numbers, within moderation always
- Helping a student is reasonable
- It’s logical for Capone to supplement share
- Reasonable grounds, mostly
- Share a line, being sensible
- Intelligent public leader goes after republican
- Well-founded desert isle with lake
Buddy explains!

The straight part
We know that "Well-founded" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case well-founded = rational.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does RATIONAL mean?
RATIONAL noun- A rational number: a number that can be expressed as the quotient of two integers.
- Capable of reasoning.
- Logically sound; not contradictory or otherwise absurd.
- (of a person or personal characteristics) Healthy or balanced intellectually; exhibiting reasonableness.
- Of a number, capable of being expressed as the ratio of two integers.
- Of an algebraic expression, capable of being expressed as the ratio of two polynomials.
- Expressing the type, structure, relations, and reactions of a compound; graphic; said of formulae.
- Expressing a physical object.
- The breastplate worn by Israelite high priests.