Whilst I agree that derivational morphology, high-register terminology and words for new concepts or objects are probably more likely to be borrowed, it is much less true to say that other stuff is 'highly unlikely' to be borrowed. It's true that it's relatively rare for something like pronouns to be borrowed into languages where they're a closed class (although in languages where there's a fuzzy noun-pronoun distinction and where using new pronominal-style expressions is easier it is much more possible). However, low-register vocabulary, certain types of inflectional morphology, prepositions and function words of all kinds are very frequently borrowed by different languages.
You can see this with English - whilst the prototypical French words are indeed high-register ones, you'll notice that lots of colloquial and everyday vocabulary is also derived from French borrowings - 'notice', for example, or 'example', or perhaps even more strikingly stuff like 'perhaps' or 'because'. Likewise, we use at least some non-Germanic inflectional morphology - most obviously plural forms in largely high-register vocabulary, but still.
The penetration of the vocabulary of a language (and its structures and everything else) will depend hugely on the type of contact. I actually don't know enough about the sociolinguistics of early Norman England to explain the English situation (although a lot of our French and Latinate vocabulary actually came in later via intellectuals I think). But I can give you some examples from different contact situations.
One example is Welsh. Welsh has been in a situation of intense, pervasive contact with the prestige language English for a very, very long time. Knowledge of English has been common in Wales for a long time, and especially in the areas closer to England English speakers and Welsh speakers have lived alongside one another and interacted forever. The important dynamics here are English's position of prestige and, more importantly, very dense contact at all levels of society (not simply for example a bilingual class of intellectuals or something). As a result, Welsh is absolutely chock full of English vocabulary, especially on the level of everyday words, as well as calqued English expressions. We have some borrowed morphology (infinitive endings dating back to Middle English or further, and plural endings), and English words for all sorts of everyday stuff (albeit sometimes borrowed long enough ago that they reflect older English forms, like giât 'gate').
Another example is Persian. Persian started out as a relatively boring classical IE language, but for a very long time has been in close contact with Turkic languages. Perhaps as a result, we can identify all sorts of sweeping typological similarities between Turkic and standard Iranian Persian - its inflectional system has been basically reworked by massive analogy to be agglutinative (if not hugely synthetic) and consist of several sets of similar but slightly distinct personal affixes, it's verb-final, it has no gender marking (even in pronouns), it has (a limited) kind of evidentiality, etc etc. The list goes on. There's also quite a lot of everyday vocabulary derived from Turkic languages. Other dialects - especially Tajik, which is still in a very intense contact situation with Uzbek - show even more Turkic features, with Tajik + Uzbek apparently having almost identical phonologies.
However, Persian is interesting in that as well as this long-term close-contact situation, it has also been in a quite distinct kind of contact with another language: Arabic. Arabic was of course the prestige language in Iran for hundreds of years following the Islamic conquests - and in fact some of the rulers of Persia were native Arabic speakers. Even once Persian-speaking rulers were in the ascendancy again Arabic was still the 'international' language of Persian intellectuals alongside Persian. This relationship is more analogous to English, and here we see a similar pattern of borrowing - huge amounts of high-register vocabulary and derivational morphology, relatively simple inflectional borrowing (especially plural endings, but also some vestigial gender agreement and so on), and also quite a lot of creep even into everyday vocabulary. It is possible of course that as in English, many of these words began as high-register terms which ended up displacing their native equivalents.
None of these languages have particularly high-level borrowing of other languages' inflectional morphology, which requires I think a very specific situation of regular code-switching and quite similar grammars to begin with. For what it's worth though, this is something that happens. If I remember correctly, the Baltic languages borrowed some Estonian case endings (at least in limited contexts). The appearance of a dental formant for the past across lots of (apparently) unrelated languages suggests that this may have been borrowed at some point too. Syrian Arabic appears to have borrowed some of its pronouns from the local Aramaic dialect. Etc, etc.
Basically I guess the answer to your question is 'it depends on the details of the contact situation you envision'.
كان يا ما كان / يا صمت العشية / قمري هاجر في الصبح بعيدا / في العيون العسلية
tà yi póbo tsùtsùr ciivà dè!