The way I understood emptiness was through the framework elaborated by the Dalai Lama in his books. Within this framework, emptiness doesn't mean 'nothingness', but rather emptiness of intrinsic nature. This means, by the philosophy of Nagarjuna, that things are dependently originated. They arise as conditioned by cause and effect.
Also, the framework of Nagarjuna distinguishes between conventional and ultimate reality. Conventional means how things appear in the everyday, while ultimate truth is perceiving reality from a perspective of wisdom. So, for example, there are conventional realities, a chair does exist, and this is within the view of dependent origination linked with causality. However, there is an ultimate reality whereby things exist as emptiness, that is lacking intrinsic essence.
I would liken this to a chair existing as a chair (conventional) but also as interacting forces at different scopes, i.e. atoms, molecules, perceptions, etc. all interacting together in a non-definable way (ultimate).
So, to answer your question, there are people suffering in the world, but these individuals lack intrinsic essence: ultimately, when analyzed with discriminating wisdom, these individuals fail to intrinsically exist. In simple terms, there are people needing help but they exist in a way reliant on emptiness.
The Heart Sutra, once again from the Dalai Lama's books, would be definitive rather than requiring interpretation. In this sense, it explains reality from the point of view of emptiness, from ultimate reality. So, indeed, from ultimate reality nothing exists, and the Heart Sutra is elaborating upon that reality, is showing this reality. We don't need to interpret within it: ultimate reality is portrayed in it. However, the conventional reality of every day appears in stark contrast with its tenets. (But in a sense, not really. Reality is ultimate, just as atoms are 'truer' than the chair: it is our perception that shows us the conventional.)
So ANSWER PART 1: There is a conventional reality underlying the ultimate nature of phenomena. There are real dhammas like striving in this reality.
Then, I would suggest the Mahayana viewpoint emphasizes compassion. I would liken compassion and emptiness' interaction as a bunch of moths flying around a lamp. The shadows of these moths are like the suffering of beings, tied with the moths. And, sometimes these shadows reflect the moths in form (conventional) but sometimes the shadows don't even resemble the moths (ultimate). However, these are the SAME shadows, only in different moment, different aspects. Compassion is like the lamp: it always interacts with the suffering, the shadows, but not necessarily in an obvious, categorically separate way.
So, no matter if the shadows are distinct, fused into a mass, light, dark, discernible or vague: in all cases, compassion brightens and relieves suffering as the lamp dispels the shadows. What changes is whether we are categorizing the shadows as intrinsic entities, distinct dhammas (e.g. moths), or merely seeing them as they actually are: a bunch of shadows.
Hence, after this perhaps too elaborate simile, ANSWER PART 2 is that compassion targets suffering even without individual entities to strive for. It connects with suffering causing positive karma, future positive rebirth, and striving altogether.
Hopes this helps,
PS: The books I refer to are here, here, here, and here.